Documentation

Overview

    Package distuv provides univariate random distribution types.

    Index

    Examples

    Constants

    This section is empty.

    Variables

    View Source
    var UnitNormal = Normal{Mu: 0, Sigma: 1}

      UnitNormal is an instantiation of the normal distribution with Mu = 0 and Sigma = 1.

      View Source
      var UnitUniform = Uniform{Min: 0, Max: 1}

        UnitUniform is an instantiation of the uniform distribution with Min = 0 and Max = 1.

        Functions

        This section is empty.

        Types

        type AlphaStable

        type AlphaStable struct {
        	// Alpha is the stability parameter.
        	// It is valid within the range 0 < α ≤ 2.
        	Alpha float64
        	// Beta is the skewness parameter.
        	// It is valid within the range -1 ≤ β ≤ 1.
        	Beta float64
        	// C is the scale parameter.
        	// It is valid when positive.
        	C float64
        	// Mu is the location parameter.
        	Mu  float64
        	Src rand.Source
        }

          AlphaStable represents an α-stable distribution with four parameters. See https://en.wikipedia.org/wiki/Stable_distribution for more information.

          func (AlphaStable) ExKurtosis

          func (a AlphaStable) ExKurtosis() float64

            ExKurtosis returns the excess kurtosis of the distribution. ExKurtosis returns NaN when Alpha != 2.

            func (AlphaStable) Mean

            func (a AlphaStable) Mean() float64

              Mean returns the mean of the probability distribution. Mean returns NaN when Alpha <= 1.

              func (AlphaStable) Median

              func (a AlphaStable) Median() float64

                Median returns the median of the distribution. Median panics when Beta != 0, because then the mode is not analytically expressible.

                func (AlphaStable) Mode

                func (a AlphaStable) Mode() float64

                  Mode returns the mode of the distribution. Mode panics when Beta != 0, because then the mode is not analytically expressible.

                  func (AlphaStable) NumParameters

                  func (a AlphaStable) NumParameters() int

                    NumParameters returns the number of parameters in the distribution.

                    func (AlphaStable) Rand

                    func (a AlphaStable) Rand() float64

                      Rand returns a random sample drawn from the distribution.

                      func (AlphaStable) Skewness

                      func (a AlphaStable) Skewness() float64

                        Skewness returns the skewness of the distribution. Skewness returns NaN when Alpha != 2.

                        func (AlphaStable) StdDev

                        func (a AlphaStable) StdDev() float64

                          StdDev returns the standard deviation of the probability distribution.

                          func (AlphaStable) Variance

                          func (a AlphaStable) Variance() float64

                            Variance returns the variance of the probability distribution. Variance returns +Inf when Alpha != 2.

                            type Bernoulli

                            type Bernoulli struct {
                            	P   float64
                            	Src rand.Source
                            }

                              Bernoulli represents a random variable whose value is 1 with probability p and value of zero with probability 1-P. The value of P must be between 0 and 1. More information at https://en.wikipedia.org/wiki/Bernoulli_distribution.

                              func (Bernoulli) CDF

                              func (b Bernoulli) CDF(x float64) float64

                                CDF computes the value of the cumulative density function at x.

                                func (Bernoulli) Entropy

                                func (b Bernoulli) Entropy() float64

                                  Entropy returns the entropy of the distribution.

                                  func (Bernoulli) ExKurtosis

                                  func (b Bernoulli) ExKurtosis() float64

                                    ExKurtosis returns the excess kurtosis of the distribution.

                                    func (Bernoulli) LogProb

                                    func (b Bernoulli) LogProb(x float64) float64

                                      LogProb computes the natural logarithm of the value of the probability density function at x.

                                      func (Bernoulli) Mean

                                      func (b Bernoulli) Mean() float64

                                        Mean returns the mean of the probability distribution.

                                        func (Bernoulli) Median

                                        func (b Bernoulli) Median() float64

                                          Median returns the median of the probability distribution.

                                          func (Bernoulli) NumParameters

                                          func (Bernoulli) NumParameters() int

                                            NumParameters returns the number of parameters in the distribution.

                                            func (Bernoulli) Prob

                                            func (b Bernoulli) Prob(x float64) float64

                                              Prob computes the value of the probability distribution at x.

                                              func (Bernoulli) Quantile

                                              func (b Bernoulli) Quantile(p float64) float64

                                                Quantile returns the minimum value of x from amongst all those values whose CDF value exceeds or equals p.

                                                func (Bernoulli) Rand

                                                func (b Bernoulli) Rand() float64

                                                  Rand returns a random sample drawn from the distribution.

                                                  func (Bernoulli) Skewness

                                                  func (b Bernoulli) Skewness() float64

                                                    Skewness returns the skewness of the distribution.

                                                    func (Bernoulli) StdDev

                                                    func (b Bernoulli) StdDev() float64

                                                      StdDev returns the standard deviation of the probability distribution.

                                                      func (Bernoulli) Survival

                                                      func (b Bernoulli) Survival(x float64) float64

                                                        Survival returns the survival function (complementary CDF) at x.

                                                        func (Bernoulli) Variance

                                                        func (b Bernoulli) Variance() float64

                                                          Variance returns the variance of the probability distribution.

                                                          type Beta

                                                          type Beta struct {
                                                          	// Alpha is the left shape parameter of the distribution. Alpha must be greater
                                                          	// than 0.
                                                          	Alpha float64
                                                          	// Beta is the right shape parameter of the distribution. Beta must be greater
                                                          	// than 0.
                                                          	Beta float64
                                                          
                                                          	Src rand.Source
                                                          }

                                                            Beta implements the Beta distribution, a two-parameter continuous distribution with support between 0 and 1.

                                                            The beta distribution has density function

                                                            x^(α-1) * (1-x)^(β-1) * Γ(α+β) / (Γ(α)*Γ(β))
                                                            

                                                            For more information, see https://en.wikipedia.org/wiki/Beta_distribution

                                                            func (Beta) CDF

                                                            func (b Beta) CDF(x float64) float64

                                                              CDF computes the value of the cumulative distribution function at x.

                                                              func (Beta) Entropy

                                                              func (b Beta) Entropy() float64

                                                                Entropy returns the differential entropy of the distribution.

                                                                func (Beta) ExKurtosis

                                                                func (b Beta) ExKurtosis() float64

                                                                  ExKurtosis returns the excess kurtosis of the distribution.

                                                                  func (Beta) LogProb

                                                                  func (b Beta) LogProb(x float64) float64

                                                                    LogProb computes the natural logarithm of the value of the probability density function at x.

                                                                    func (Beta) Mean

                                                                    func (b Beta) Mean() float64

                                                                      Mean returns the mean of the probability distribution.

                                                                      func (Beta) Mode

                                                                      func (b Beta) Mode() float64

                                                                        Mode returns the mode of the distribution.

                                                                        Mode returns NaN if both parametera are less than or equal to 1 as a special case, 0 if only Alpha <= 1 and 1 if only Beta <= 1.

                                                                        func (Beta) NumParameters

                                                                        func (b Beta) NumParameters() int

                                                                          NumParameters returns the number of parameters in the distribution.

                                                                          func (Beta) Prob

                                                                          func (b Beta) Prob(x float64) float64

                                                                            Prob computes the value of the probability density function at x.

                                                                            func (Beta) Quantile

                                                                            func (b Beta) Quantile(p float64) float64

                                                                              Quantile returns the inverse of the cumulative distribution function.

                                                                              func (Beta) Rand

                                                                              func (b Beta) Rand() float64

                                                                                Rand returns a random sample drawn from the distribution.

                                                                                func (Beta) StdDev

                                                                                func (b Beta) StdDev() float64

                                                                                  StdDev returns the standard deviation of the probability distribution.

                                                                                  func (Beta) Survival

                                                                                  func (b Beta) Survival(x float64) float64

                                                                                    Survival returns the survival function (complementary CDF) at x.

                                                                                    func (Beta) Variance

                                                                                    func (b Beta) Variance() float64

                                                                                      Variance returns the variance of the probability distribution.

                                                                                      type Bhattacharyya

                                                                                      type Bhattacharyya struct{}

                                                                                        Bhattacharyya is a type for computing the Bhattacharyya distance between probability distributions.

                                                                                        The Bhattacharyya distance is defined as

                                                                                        D_B = -ln(BC(l,r))
                                                                                        BC = \int_-∞^∞ (p(x)q(x))^(1/2) dx
                                                                                        

                                                                                        Where BC is known as the Bhattacharyya coefficient. The Bhattacharyya distance is related to the Hellinger distance by

                                                                                        H(l,r) = sqrt(1-BC(l,r))
                                                                                        

                                                                                        For more information, see

                                                                                        https://en.wikipedia.org/wiki/Bhattacharyya_distance
                                                                                        

                                                                                        func (Bhattacharyya) DistBeta

                                                                                        func (Bhattacharyya) DistBeta(l, r Beta) float64

                                                                                          DistBeta returns the Bhattacharyya distance between Beta distributions l and r. For Beta distributions, the Bhattacharyya distance is given by

                                                                                          -ln(B((α_l + α_r)/2, (β_l + β_r)/2) / (B(α_l,β_l), B(α_r,β_r)))
                                                                                          

                                                                                          Where B is the Beta function.

                                                                                          func (Bhattacharyya) DistNormal

                                                                                          func (Bhattacharyya) DistNormal(l, r Normal) float64

                                                                                            DistNormal returns the Bhattacharyya distance Normal distributions l and r. For Normal distributions, the Bhattacharyya distance is given by

                                                                                            s = (σ_l^2 + σ_r^2)/2
                                                                                            BC = 1/8 (μ_l-μ_r)^2/s + 1/2 ln(s/(σ_l*σ_r))
                                                                                            

                                                                                            type Binomial

                                                                                            type Binomial struct {
                                                                                            	// N is the total number of Bernoulli trials. N must be greater than 0.
                                                                                            	N float64
                                                                                            	// P is the probability of success in any given trial. P must be in [0, 1].
                                                                                            	P float64
                                                                                            
                                                                                            	Src rand.Source
                                                                                            }

                                                                                              Binomial implements the binomial distribution, a discrete probability distribution that expresses the probability of a given number of successful Bernoulli trials out of a total of n, each with success probability p. The binomial distribution has the density function:

                                                                                              f(k) = (n choose k) p^k (1-p)^(n-k)
                                                                                              

                                                                                              For more information, see https://en.wikipedia.org/wiki/Binomial_distribution.

                                                                                              func (Binomial) CDF

                                                                                              func (b Binomial) CDF(x float64) float64

                                                                                                CDF computes the value of the cumulative distribution function at x.

                                                                                                func (Binomial) ExKurtosis

                                                                                                func (b Binomial) ExKurtosis() float64

                                                                                                  ExKurtosis returns the excess kurtosis of the distribution.

                                                                                                  func (Binomial) LogProb

                                                                                                  func (b Binomial) LogProb(x float64) float64

                                                                                                    LogProb computes the natural logarithm of the value of the probability density function at x.

                                                                                                    func (Binomial) Mean

                                                                                                    func (b Binomial) Mean() float64

                                                                                                      Mean returns the mean of the probability distribution.

                                                                                                      func (Binomial) NumParameters

                                                                                                      func (Binomial) NumParameters() int

                                                                                                        NumParameters returns the number of parameters in the distribution.

                                                                                                        func (Binomial) Prob

                                                                                                        func (b Binomial) Prob(x float64) float64

                                                                                                          Prob computes the value of the probability density function at x.

                                                                                                          func (Binomial) Rand

                                                                                                          func (b Binomial) Rand() float64

                                                                                                            Rand returns a random sample drawn from the distribution.

                                                                                                            func (Binomial) Skewness

                                                                                                            func (b Binomial) Skewness() float64

                                                                                                              Skewness returns the skewness of the distribution.

                                                                                                              func (Binomial) StdDev

                                                                                                              func (b Binomial) StdDev() float64

                                                                                                                StdDev returns the standard deviation of the probability distribution.

                                                                                                                func (Binomial) Survival

                                                                                                                func (b Binomial) Survival(x float64) float64

                                                                                                                  Survival returns the survival function (complementary CDF) at x.

                                                                                                                  func (Binomial) Variance

                                                                                                                  func (b Binomial) Variance() float64

                                                                                                                    Variance returns the variance of the probability distribution.

                                                                                                                    type Categorical

                                                                                                                    type Categorical struct {
                                                                                                                    	// contains filtered or unexported fields
                                                                                                                    }

                                                                                                                      Categorical is an extension of the Bernoulli distribution where x takes values {0, 1, ..., len(w)-1} where w is the weight vector. Categorical must be initialized with NewCategorical.

                                                                                                                      func NewCategorical

                                                                                                                      func NewCategorical(w []float64, src rand.Source) Categorical

                                                                                                                        NewCategorical constructs a new categorical distribution where the probability that x equals i is proportional to w[i]. All of the weights must be nonnegative, and at least one of the weights must be positive.

                                                                                                                        func (Categorical) CDF

                                                                                                                        func (c Categorical) CDF(x float64) float64

                                                                                                                          CDF computes the value of the cumulative density function at x.

                                                                                                                          func (Categorical) Entropy

                                                                                                                          func (c Categorical) Entropy() float64

                                                                                                                            Entropy returns the entropy of the distribution.

                                                                                                                            func (Categorical) Len

                                                                                                                            func (c Categorical) Len() int

                                                                                                                              Len returns the number of values x could possibly take (the length of the initial supplied weight vector).

                                                                                                                              func (Categorical) LogProb

                                                                                                                              func (c Categorical) LogProb(x float64) float64

                                                                                                                                LogProb computes the natural logarithm of the value of the probability density function at x.

                                                                                                                                func (Categorical) Mean

                                                                                                                                func (c Categorical) Mean() float64

                                                                                                                                  Mean returns the mean of the probability distribution.

                                                                                                                                  func (Categorical) Prob

                                                                                                                                  func (c Categorical) Prob(x float64) float64

                                                                                                                                    Prob computes the value of the probability density function at x.

                                                                                                                                    func (Categorical) Rand

                                                                                                                                    func (c Categorical) Rand() float64

                                                                                                                                      Rand returns a random draw from the categorical distribution.

                                                                                                                                      func (Categorical) Reweight

                                                                                                                                      func (c Categorical) Reweight(idx int, w float64)

                                                                                                                                        Reweight sets the weight of item idx to w. The input weight must be non-negative, and after reweighting at least one of the weights must be positive.

                                                                                                                                        func (Categorical) ReweightAll

                                                                                                                                        func (c Categorical) ReweightAll(w []float64)

                                                                                                                                          ReweightAll resets the weights of the distribution. ReweightAll panics if len(w) != c.Len. All of the weights must be nonnegative, and at least one of the weights must be positive.

                                                                                                                                          type ChiSquared

                                                                                                                                          type ChiSquared struct {
                                                                                                                                          	// K is the shape parameter, corresponding to the degrees of freedom. Must
                                                                                                                                          	// be greater than 0.
                                                                                                                                          	K float64
                                                                                                                                          
                                                                                                                                          	Src rand.Source
                                                                                                                                          }

                                                                                                                                            ChiSquared implements the χ² distribution, a one parameter distribution with support on the positive numbers.

                                                                                                                                            The density function is given by

                                                                                                                                            1/(2^{k/2} * Γ(k/2)) * x^{k/2 - 1} * e^{-x/2}
                                                                                                                                            

                                                                                                                                            It is a special case of the Gamma distribution, Γ(k/2, 1/2).

                                                                                                                                            For more information, see https://en.wikipedia.org/wiki/Chi-squared_distribution.

                                                                                                                                            func (ChiSquared) CDF

                                                                                                                                            func (c ChiSquared) CDF(x float64) float64

                                                                                                                                              CDF computes the value of the cumulative density function at x.

                                                                                                                                              func (ChiSquared) ExKurtosis

                                                                                                                                              func (c ChiSquared) ExKurtosis() float64

                                                                                                                                                ExKurtosis returns the excess kurtosis of the distribution.

                                                                                                                                                func (ChiSquared) LogProb

                                                                                                                                                func (c ChiSquared) LogProb(x float64) float64

                                                                                                                                                  LogProb computes the natural logarithm of the value of the probability density function at x.

                                                                                                                                                  func (ChiSquared) Mean

                                                                                                                                                  func (c ChiSquared) Mean() float64

                                                                                                                                                    Mean returns the mean of the probability distribution.

                                                                                                                                                    func (ChiSquared) Mode

                                                                                                                                                    func (c ChiSquared) Mode() float64

                                                                                                                                                      Mode returns the mode of the distribution.

                                                                                                                                                      func (ChiSquared) NumParameters

                                                                                                                                                      func (c ChiSquared) NumParameters() int

                                                                                                                                                        NumParameters returns the number of parameters in the distribution.

                                                                                                                                                        func (ChiSquared) Prob

                                                                                                                                                        func (c ChiSquared) Prob(x float64) float64

                                                                                                                                                          Prob computes the value of the probability density function at x.

                                                                                                                                                          func (ChiSquared) Quantile

                                                                                                                                                          func (c ChiSquared) Quantile(p float64) float64

                                                                                                                                                            Quantile returns the inverse of the cumulative distribution function.

                                                                                                                                                            func (ChiSquared) Rand

                                                                                                                                                            func (c ChiSquared) Rand() float64

                                                                                                                                                              Rand returns a random sample drawn from the distribution.

                                                                                                                                                              func (ChiSquared) StdDev

                                                                                                                                                              func (c ChiSquared) StdDev() float64

                                                                                                                                                                StdDev returns the standard deviation of the probability distribution.

                                                                                                                                                                func (ChiSquared) Survival

                                                                                                                                                                func (c ChiSquared) Survival(x float64) float64

                                                                                                                                                                  Survival returns the survival function (complementary CDF) at x.

                                                                                                                                                                  func (ChiSquared) Variance

                                                                                                                                                                  func (c ChiSquared) Variance() float64

                                                                                                                                                                    Variance returns the variance of the probability distribution.

                                                                                                                                                                    type Exponential

                                                                                                                                                                    type Exponential struct {
                                                                                                                                                                    	Rate float64
                                                                                                                                                                    	Src  rand.Source
                                                                                                                                                                    }

                                                                                                                                                                      Exponential represents the exponential distribution (https://en.wikipedia.org/wiki/Exponential_distribution).

                                                                                                                                                                      func (Exponential) CDF

                                                                                                                                                                      func (e Exponential) CDF(x float64) float64

                                                                                                                                                                        CDF computes the value of the cumulative density function at x.

                                                                                                                                                                        func (*Exponential) ConjugateUpdate

                                                                                                                                                                        func (e *Exponential) ConjugateUpdate(suffStat []float64, nSamples float64, priorStrength []float64)

                                                                                                                                                                          ConjugateUpdate updates the parameters of the distribution from the sufficient statistics of a set of samples. The sufficient statistics, suffStat, have been observed with nSamples observations. The prior values of the distribution are those currently in the distribution, and have been observed with priorStrength samples.

                                                                                                                                                                          For the exponential distribution, the sufficient statistic is the inverse of the mean of the samples. The prior is having seen priorStrength[0] samples with inverse mean Exponential.Rate As a result of this function, Exponential.Rate is updated based on the weighted samples, and priorStrength is modified to include the new number of samples observed.

                                                                                                                                                                          This function panics if len(suffStat) != e.NumSuffStat() or len(priorStrength) != e.NumSuffStat().

                                                                                                                                                                          func (Exponential) Entropy

                                                                                                                                                                          func (e Exponential) Entropy() float64

                                                                                                                                                                            Entropy returns the entropy of the distribution.

                                                                                                                                                                            func (Exponential) ExKurtosis

                                                                                                                                                                            func (Exponential) ExKurtosis() float64

                                                                                                                                                                              ExKurtosis returns the excess kurtosis of the distribution.

                                                                                                                                                                              func (*Exponential) Fit

                                                                                                                                                                              func (e *Exponential) Fit(samples, weights []float64)

                                                                                                                                                                                Fit sets the parameters of the probability distribution from the data samples x with relative weights w. If weights is nil, then all the weights are 1. If weights is not nil, then the len(weights) must equal len(samples).

                                                                                                                                                                                func (Exponential) LogProb

                                                                                                                                                                                func (e Exponential) LogProb(x float64) float64

                                                                                                                                                                                  LogProb computes the natural logarithm of the value of the probability density function at x.

                                                                                                                                                                                  func (Exponential) Mean

                                                                                                                                                                                  func (e Exponential) Mean() float64

                                                                                                                                                                                    Mean returns the mean of the probability distribution.

                                                                                                                                                                                    func (Exponential) Median

                                                                                                                                                                                    func (e Exponential) Median() float64

                                                                                                                                                                                      Median returns the median of the probability distribution.

                                                                                                                                                                                      func (Exponential) Mode

                                                                                                                                                                                      func (Exponential) Mode() float64

                                                                                                                                                                                        Mode returns the mode of the probability distribution.

                                                                                                                                                                                        func (Exponential) NumParameters

                                                                                                                                                                                        func (Exponential) NumParameters() int

                                                                                                                                                                                          NumParameters returns the number of parameters in the distribution.

                                                                                                                                                                                          func (Exponential) NumSuffStat

                                                                                                                                                                                          func (Exponential) NumSuffStat() int

                                                                                                                                                                                            NumSuffStat returns the number of sufficient statistics for the distribution.

                                                                                                                                                                                            func (Exponential) Prob

                                                                                                                                                                                            func (e Exponential) Prob(x float64) float64

                                                                                                                                                                                              Prob computes the value of the probability density function at x.

                                                                                                                                                                                              func (Exponential) Quantile

                                                                                                                                                                                              func (e Exponential) Quantile(p float64) float64

                                                                                                                                                                                                Quantile returns the inverse of the cumulative probability distribution.

                                                                                                                                                                                                func (Exponential) Rand

                                                                                                                                                                                                func (e Exponential) Rand() float64

                                                                                                                                                                                                  Rand returns a random sample drawn from the distribution.

                                                                                                                                                                                                  func (Exponential) Score

                                                                                                                                                                                                  func (e Exponential) Score(deriv []float64, x float64) []float64

                                                                                                                                                                                                    Score returns the score function with respect to the parameters of the distribution at the input location x. The score function is the derivative of the log-likelihood at x with respect to the parameters

                                                                                                                                                                                                    (∂/∂θ) log(p(x;θ))
                                                                                                                                                                                                    

                                                                                                                                                                                                    If deriv is non-nil, len(deriv) must equal the number of parameters otherwise Score will panic, and the derivative is stored in-place into deriv. If deriv is nil a new slice will be allocated and returned.

                                                                                                                                                                                                    The order is [∂LogProb / ∂Rate].

                                                                                                                                                                                                    For more information, see https://en.wikipedia.org/wiki/Score_%28statistics%29.

                                                                                                                                                                                                    Special cases:

                                                                                                                                                                                                    Score(0) = [NaN]
                                                                                                                                                                                                    

                                                                                                                                                                                                    func (Exponential) ScoreInput

                                                                                                                                                                                                    func (e Exponential) ScoreInput(x float64) float64

                                                                                                                                                                                                      ScoreInput returns the score function with respect to the input of the distribution at the input location specified by x. The score function is the derivative of the log-likelihood

                                                                                                                                                                                                      (d/dx) log(p(x)) .
                                                                                                                                                                                                      

                                                                                                                                                                                                      Special cases:

                                                                                                                                                                                                      ScoreInput(0) = NaN
                                                                                                                                                                                                      

                                                                                                                                                                                                      func (Exponential) Skewness

                                                                                                                                                                                                      func (Exponential) Skewness() float64

                                                                                                                                                                                                        Skewness returns the skewness of the distribution.

                                                                                                                                                                                                        func (Exponential) StdDev

                                                                                                                                                                                                        func (e Exponential) StdDev() float64

                                                                                                                                                                                                          StdDev returns the standard deviation of the probability distribution.

                                                                                                                                                                                                          func (Exponential) SuffStat

                                                                                                                                                                                                          func (Exponential) SuffStat(suffStat, samples, weights []float64) (nSamples float64)

                                                                                                                                                                                                            SuffStat computes the sufficient statistics of set of samples to update the distribution. The sufficient statistics are stored in place, and the effective number of samples are returned.

                                                                                                                                                                                                            The exponential distribution has one sufficient statistic, the average rate of the samples.

                                                                                                                                                                                                            If weights is nil, the weights are assumed to be 1, otherwise panics if len(samples) != len(weights). Panics if len(suffStat) != NumSuffStat().

                                                                                                                                                                                                            func (Exponential) Survival

                                                                                                                                                                                                            func (e Exponential) Survival(x float64) float64

                                                                                                                                                                                                              Survival returns the survival function (complementary CDF) at x.

                                                                                                                                                                                                              func (Exponential) Variance

                                                                                                                                                                                                              func (e Exponential) Variance() float64

                                                                                                                                                                                                                Variance returns the variance of the probability distribution.

                                                                                                                                                                                                                type F

                                                                                                                                                                                                                type F struct {
                                                                                                                                                                                                                	D1  float64 // Degrees of freedom for the numerator
                                                                                                                                                                                                                	D2  float64 // Degrees of freedom for the denominator
                                                                                                                                                                                                                	Src rand.Source
                                                                                                                                                                                                                }

                                                                                                                                                                                                                  F implements the F-distribution, a two-parameter continuous distribution with support over the positive real numbers.

                                                                                                                                                                                                                  The F-distribution has density function

                                                                                                                                                                                                                  sqrt(((d1*x)^d1) * d2^d2 / ((d1*x+d2)^(d1+d2))) / (x * B(d1/2,d2/2))
                                                                                                                                                                                                                  

                                                                                                                                                                                                                  where B is the beta function.

                                                                                                                                                                                                                  For more information, see https://en.wikipedia.org/wiki/F-distribution

                                                                                                                                                                                                                  func (F) CDF

                                                                                                                                                                                                                  func (f F) CDF(x float64) float64

                                                                                                                                                                                                                    CDF computes the value of the cumulative density function at x.

                                                                                                                                                                                                                    func (F) ExKurtosis

                                                                                                                                                                                                                    func (f F) ExKurtosis() float64

                                                                                                                                                                                                                      ExKurtosis returns the excess kurtosis of the distribution.

                                                                                                                                                                                                                      ExKurtosis returns NaN if the D2 parameter is less or equal to 8.

                                                                                                                                                                                                                      func (F) LogProb

                                                                                                                                                                                                                      func (f F) LogProb(x float64) float64

                                                                                                                                                                                                                        LogProb computes the natural logarithm of the value of the probability density function at x.

                                                                                                                                                                                                                        func (F) Mean

                                                                                                                                                                                                                        func (f F) Mean() float64

                                                                                                                                                                                                                          Mean returns the mean of the probability distribution.

                                                                                                                                                                                                                          Mean returns NaN if the D2 parameter is less than or equal to 2.

                                                                                                                                                                                                                          func (F) Mode

                                                                                                                                                                                                                          func (f F) Mode() float64

                                                                                                                                                                                                                            Mode returns the mode of the distribution.

                                                                                                                                                                                                                            Mode returns NaN if the D1 parameter is less than or equal to 2.

                                                                                                                                                                                                                            func (F) NumParameters

                                                                                                                                                                                                                            func (f F) NumParameters() int

                                                                                                                                                                                                                              NumParameters returns the number of parameters in the distribution.

                                                                                                                                                                                                                              func (F) Prob

                                                                                                                                                                                                                              func (f F) Prob(x float64) float64

                                                                                                                                                                                                                                Prob computes the value of the probability density function at x.

                                                                                                                                                                                                                                func (F) Quantile

                                                                                                                                                                                                                                func (f F) Quantile(p float64) float64

                                                                                                                                                                                                                                  Quantile returns the inverse of the cumulative distribution function.

                                                                                                                                                                                                                                  func (F) Rand

                                                                                                                                                                                                                                  func (f F) Rand() float64

                                                                                                                                                                                                                                    Rand returns a random sample drawn from the distribution.

                                                                                                                                                                                                                                    func (F) Skewness

                                                                                                                                                                                                                                    func (f F) Skewness() float64

                                                                                                                                                                                                                                      Skewness returns the skewness of the distribution.

                                                                                                                                                                                                                                      Skewness returns NaN if the D2 parameter is less than or equal to 6.

                                                                                                                                                                                                                                      func (F) StdDev

                                                                                                                                                                                                                                      func (f F) StdDev() float64

                                                                                                                                                                                                                                        StdDev returns the standard deviation of the probability distribution.

                                                                                                                                                                                                                                        StdDev returns NaN if the D2 parameter is less than or equal to 4.

                                                                                                                                                                                                                                        func (F) Survival

                                                                                                                                                                                                                                        func (f F) Survival(x float64) float64

                                                                                                                                                                                                                                          Survival returns the survival function (complementary CDF) at x.

                                                                                                                                                                                                                                          func (F) Variance

                                                                                                                                                                                                                                          func (f F) Variance() float64

                                                                                                                                                                                                                                            Variance returns the variance of the probability distribution.

                                                                                                                                                                                                                                            Variance returns NaN if the D2 parameter is less than or equal to 4.

                                                                                                                                                                                                                                            type Gamma

                                                                                                                                                                                                                                            type Gamma struct {
                                                                                                                                                                                                                                            	// Alpha is the shape parameter of the distribution. Alpha must be greater
                                                                                                                                                                                                                                            	// than 0. If Alpha == 1, this is equivalent to an exponential distribution.
                                                                                                                                                                                                                                            	Alpha float64
                                                                                                                                                                                                                                            	// Beta is the rate parameter of the distribution. Beta must be greater than 0.
                                                                                                                                                                                                                                            	// If Beta == 2, this is equivalent to a Chi-Squared distribution.
                                                                                                                                                                                                                                            	Beta float64
                                                                                                                                                                                                                                            
                                                                                                                                                                                                                                            	Src rand.Source
                                                                                                                                                                                                                                            }

                                                                                                                                                                                                                                              Gamma implements the Gamma distribution, a two-parameter continuous distribution with support over the positive real numbers.

                                                                                                                                                                                                                                              The gamma distribution has density function

                                                                                                                                                                                                                                              β^α / Γ(α) x^(α-1)e^(-βx)
                                                                                                                                                                                                                                              

                                                                                                                                                                                                                                              For more information, see https://en.wikipedia.org/wiki/Gamma_distribution

                                                                                                                                                                                                                                              func (Gamma) CDF

                                                                                                                                                                                                                                              func (g Gamma) CDF(x float64) float64

                                                                                                                                                                                                                                                CDF computes the value of the cumulative distribution function at x.

                                                                                                                                                                                                                                                func (Gamma) ExKurtosis

                                                                                                                                                                                                                                                func (g Gamma) ExKurtosis() float64

                                                                                                                                                                                                                                                  ExKurtosis returns the excess kurtosis of the distribution.

                                                                                                                                                                                                                                                  func (Gamma) LogProb

                                                                                                                                                                                                                                                  func (g Gamma) LogProb(x float64) float64

                                                                                                                                                                                                                                                    LogProb computes the natural logarithm of the value of the probability density function at x.

                                                                                                                                                                                                                                                    func (Gamma) Mean

                                                                                                                                                                                                                                                    func (g Gamma) Mean() float64

                                                                                                                                                                                                                                                      Mean returns the mean of the probability distribution.

                                                                                                                                                                                                                                                      func (Gamma) Mode

                                                                                                                                                                                                                                                      func (g Gamma) Mode() float64

                                                                                                                                                                                                                                                        Mode returns the mode of the normal distribution.

                                                                                                                                                                                                                                                        The mode is NaN in the special case where the Alpha (shape) parameter is less than 1.

                                                                                                                                                                                                                                                        func (Gamma) NumParameters

                                                                                                                                                                                                                                                        func (Gamma) NumParameters() int

                                                                                                                                                                                                                                                          NumParameters returns the number of parameters in the distribution.

                                                                                                                                                                                                                                                          func (Gamma) Prob

                                                                                                                                                                                                                                                          func (g Gamma) Prob(x float64) float64

                                                                                                                                                                                                                                                            Prob computes the value of the probability density function at x.

                                                                                                                                                                                                                                                            func (Gamma) Quantile

                                                                                                                                                                                                                                                            func (g Gamma) Quantile(p float64) float64

                                                                                                                                                                                                                                                              Quantile returns the inverse of the cumulative distribution function.

                                                                                                                                                                                                                                                              func (Gamma) Rand

                                                                                                                                                                                                                                                              func (g Gamma) Rand() float64

                                                                                                                                                                                                                                                                Rand returns a random sample drawn from the distribution.

                                                                                                                                                                                                                                                                Rand panics if either alpha or beta is <= 0.

                                                                                                                                                                                                                                                                func (Gamma) StdDev

                                                                                                                                                                                                                                                                func (g Gamma) StdDev() float64

                                                                                                                                                                                                                                                                  StdDev returns the standard deviation of the probability distribution.

                                                                                                                                                                                                                                                                  func (Gamma) Survival

                                                                                                                                                                                                                                                                  func (g Gamma) Survival(x float64) float64

                                                                                                                                                                                                                                                                    Survival returns the survival function (complementary CDF) at x.

                                                                                                                                                                                                                                                                    func (Gamma) Variance

                                                                                                                                                                                                                                                                    func (g Gamma) Variance() float64

                                                                                                                                                                                                                                                                      Variance returns the variance of the probability distribution.

                                                                                                                                                                                                                                                                      type GumbelRight

                                                                                                                                                                                                                                                                      type GumbelRight struct {
                                                                                                                                                                                                                                                                      	Mu   float64
                                                                                                                                                                                                                                                                      	Beta float64
                                                                                                                                                                                                                                                                      	Src  rand.Source
                                                                                                                                                                                                                                                                      }

                                                                                                                                                                                                                                                                        GumbelRight implements the right-skewed Gumbel distribution, a two-parameter continuous distribution with support over the real numbers. The right-skewed Gumbel distribution is also sometimes known as the Extreme Value distribution.

                                                                                                                                                                                                                                                                        The right-skewed Gumbel distribution has density function

                                                                                                                                                                                                                                                                        1/beta * exp(-(z + exp(-z)))
                                                                                                                                                                                                                                                                        z = (x - mu)/beta
                                                                                                                                                                                                                                                                        

                                                                                                                                                                                                                                                                        Beta must be greater than 0.

                                                                                                                                                                                                                                                                        For more information, see https://en.wikipedia.org/wiki/Gumbel_distribution.

                                                                                                                                                                                                                                                                        func (GumbelRight) CDF

                                                                                                                                                                                                                                                                        func (g GumbelRight) CDF(x float64) float64

                                                                                                                                                                                                                                                                          CDF computes the value of the cumulative density function at x.

                                                                                                                                                                                                                                                                          func (GumbelRight) Entropy

                                                                                                                                                                                                                                                                          func (g GumbelRight) Entropy() float64

                                                                                                                                                                                                                                                                            Entropy returns the differential entropy of the distribution.

                                                                                                                                                                                                                                                                            func (GumbelRight) ExKurtosis

                                                                                                                                                                                                                                                                            func (g GumbelRight) ExKurtosis() float64

                                                                                                                                                                                                                                                                              ExKurtosis returns the excess kurtosis of the distribution.

                                                                                                                                                                                                                                                                              func (GumbelRight) LogProb

                                                                                                                                                                                                                                                                              func (g GumbelRight) LogProb(x float64) float64

                                                                                                                                                                                                                                                                                LogProb computes the natural logarithm of the value of the probability density function at x.

                                                                                                                                                                                                                                                                                func (GumbelRight) Mean

                                                                                                                                                                                                                                                                                func (g GumbelRight) Mean() float64

                                                                                                                                                                                                                                                                                  Mean returns the mean of the probability distribution.

                                                                                                                                                                                                                                                                                  func (GumbelRight) Median

                                                                                                                                                                                                                                                                                  func (g GumbelRight) Median() float64

                                                                                                                                                                                                                                                                                    Median returns the median of the Gumbel distribution.

                                                                                                                                                                                                                                                                                    func (GumbelRight) Mode

                                                                                                                                                                                                                                                                                    func (g GumbelRight) Mode() float64

                                                                                                                                                                                                                                                                                      Mode returns the mode of the normal distribution.

                                                                                                                                                                                                                                                                                      func (GumbelRight) NumParameters

                                                                                                                                                                                                                                                                                      func (GumbelRight) NumParameters() int

                                                                                                                                                                                                                                                                                        NumParameters returns the number of parameters in the distribution.

                                                                                                                                                                                                                                                                                        func (GumbelRight) Prob

                                                                                                                                                                                                                                                                                        func (g GumbelRight) Prob(x float64) float64

                                                                                                                                                                                                                                                                                          Prob computes the value of the probability density function at x.

                                                                                                                                                                                                                                                                                          func (GumbelRight) Quantile

                                                                                                                                                                                                                                                                                          func (g GumbelRight) Quantile(p float64) float64

                                                                                                                                                                                                                                                                                            Quantile returns the inverse of the cumulative probability distribution.

                                                                                                                                                                                                                                                                                            func (GumbelRight) Rand

                                                                                                                                                                                                                                                                                            func (g GumbelRight) Rand() float64

                                                                                                                                                                                                                                                                                              Rand returns a random sample drawn from the distribution.

                                                                                                                                                                                                                                                                                              func (GumbelRight) Skewness

                                                                                                                                                                                                                                                                                              func (GumbelRight) Skewness() float64

                                                                                                                                                                                                                                                                                                Skewness returns the skewness of the distribution.

                                                                                                                                                                                                                                                                                                func (GumbelRight) StdDev

                                                                                                                                                                                                                                                                                                func (g GumbelRight) StdDev() float64

                                                                                                                                                                                                                                                                                                  StdDev returns the standard deviation of the probability distribution.

                                                                                                                                                                                                                                                                                                  func (GumbelRight) Survival

                                                                                                                                                                                                                                                                                                  func (g GumbelRight) Survival(x float64) float64

                                                                                                                                                                                                                                                                                                    Survival returns the survival function (complementary CDF) at x.

                                                                                                                                                                                                                                                                                                    func (GumbelRight) Variance

                                                                                                                                                                                                                                                                                                    func (g GumbelRight) Variance() float64

                                                                                                                                                                                                                                                                                                      Variance returns the variance of the probability distribution.

                                                                                                                                                                                                                                                                                                      type Hellinger

                                                                                                                                                                                                                                                                                                      type Hellinger struct{}

                                                                                                                                                                                                                                                                                                        Hellinger is a type for computing the Hellinger distance between probability distributions.

                                                                                                                                                                                                                                                                                                        The Hellinger distance is defined as

                                                                                                                                                                                                                                                                                                        H^2(l,r) = 1/2 * int_x (\sqrt(l(x)) - \sqrt(r(x)))^2 dx
                                                                                                                                                                                                                                                                                                        

                                                                                                                                                                                                                                                                                                        and is bounded between 0 and 1. Note the above formula defines the squared Hellinger distance, while this returns the Hellinger distance itself. The Hellinger distance is related to the Bhattacharyya distance by

                                                                                                                                                                                                                                                                                                        H^2 = 1 - exp(-D_B)
                                                                                                                                                                                                                                                                                                        

                                                                                                                                                                                                                                                                                                        For more information, see

                                                                                                                                                                                                                                                                                                        https://en.wikipedia.org/wiki/Hellinger_distance
                                                                                                                                                                                                                                                                                                        

                                                                                                                                                                                                                                                                                                        func (Hellinger) DistBeta

                                                                                                                                                                                                                                                                                                        func (Hellinger) DistBeta(l, r Beta) float64

                                                                                                                                                                                                                                                                                                          DistBeta computes the Hellinger distance between Beta distributions l and r. See the documentation of Bhattacharyya.DistBeta for the distance formula.

                                                                                                                                                                                                                                                                                                          func (Hellinger) DistNormal

                                                                                                                                                                                                                                                                                                          func (Hellinger) DistNormal(l, r Normal) float64

                                                                                                                                                                                                                                                                                                            DistNormal computes the Hellinger distance between Normal distributions l and r. See the documentation of Bhattacharyya.DistNormal for the distance formula.

                                                                                                                                                                                                                                                                                                            type InverseGamma

                                                                                                                                                                                                                                                                                                            type InverseGamma struct {
                                                                                                                                                                                                                                                                                                            	// Alpha is the shape parameter of the distribution. Alpha must be greater than 0.
                                                                                                                                                                                                                                                                                                            	Alpha float64
                                                                                                                                                                                                                                                                                                            	// Beta is the scale parameter of the distribution. Beta must be greater than 0.
                                                                                                                                                                                                                                                                                                            	Beta float64
                                                                                                                                                                                                                                                                                                            
                                                                                                                                                                                                                                                                                                            	Src rand.Source
                                                                                                                                                                                                                                                                                                            }

                                                                                                                                                                                                                                                                                                              InverseGamma implements the inverse gamma distribution, a two-parameter continuous distribution with support over the positive real numbers. The inverse gamma distribution is the same as the distribution of the reciprocal of a gamma distributed random variable.

                                                                                                                                                                                                                                                                                                              The inverse gamma distribution has density function

                                                                                                                                                                                                                                                                                                              β^α / Γ(α) x^(-α-1)e^(-β/x)
                                                                                                                                                                                                                                                                                                              

                                                                                                                                                                                                                                                                                                              For more information, see https://en.wikipedia.org/wiki/Inverse-gamma_distribution

                                                                                                                                                                                                                                                                                                              func (InverseGamma) CDF

                                                                                                                                                                                                                                                                                                              func (g InverseGamma) CDF(x float64) float64

                                                                                                                                                                                                                                                                                                                CDF computes the value of the cumulative distribution function at x.

                                                                                                                                                                                                                                                                                                                func (InverseGamma) ExKurtosis

                                                                                                                                                                                                                                                                                                                func (g InverseGamma) ExKurtosis() float64

                                                                                                                                                                                                                                                                                                                  ExKurtosis returns the excess kurtosis of the distribution.

                                                                                                                                                                                                                                                                                                                  func (InverseGamma) LogProb

                                                                                                                                                                                                                                                                                                                  func (g InverseGamma) LogProb(x float64) float64

                                                                                                                                                                                                                                                                                                                    LogProb computes the natural logarithm of the value of the probability density function at x.

                                                                                                                                                                                                                                                                                                                    func (InverseGamma) Mean

                                                                                                                                                                                                                                                                                                                    func (g InverseGamma) Mean() float64

                                                                                                                                                                                                                                                                                                                      Mean returns the mean of the probability distribution.

                                                                                                                                                                                                                                                                                                                      func (InverseGamma) Mode

                                                                                                                                                                                                                                                                                                                      func (g InverseGamma) Mode() float64

                                                                                                                                                                                                                                                                                                                        Mode returns the mode of the distribution.

                                                                                                                                                                                                                                                                                                                        func (InverseGamma) NumParameters

                                                                                                                                                                                                                                                                                                                        func (InverseGamma) NumParameters() int

                                                                                                                                                                                                                                                                                                                          NumParameters returns the number of parameters in the distribution.

                                                                                                                                                                                                                                                                                                                          func (InverseGamma) Prob

                                                                                                                                                                                                                                                                                                                          func (g InverseGamma) Prob(x float64) float64

                                                                                                                                                                                                                                                                                                                            Prob computes the value of the probability density function at x.

                                                                                                                                                                                                                                                                                                                            func (InverseGamma) Quantile

                                                                                                                                                                                                                                                                                                                            func (g InverseGamma) Quantile(p float64) float64

                                                                                                                                                                                                                                                                                                                              Quantile returns the inverse of the cumulative distribution function.

                                                                                                                                                                                                                                                                                                                              func (InverseGamma) Rand

                                                                                                                                                                                                                                                                                                                              func (g InverseGamma) Rand() float64

                                                                                                                                                                                                                                                                                                                                Rand returns a random sample drawn from the distribution.

                                                                                                                                                                                                                                                                                                                                Rand panics if either alpha or beta is <= 0.

                                                                                                                                                                                                                                                                                                                                func (InverseGamma) StdDev

                                                                                                                                                                                                                                                                                                                                func (g InverseGamma) StdDev() float64

                                                                                                                                                                                                                                                                                                                                  StdDev returns the standard deviation of the probability distribution.

                                                                                                                                                                                                                                                                                                                                  func (InverseGamma) Survival

                                                                                                                                                                                                                                                                                                                                  func (g InverseGamma) Survival(x float64) float64

                                                                                                                                                                                                                                                                                                                                    Survival returns the survival function (complementary CDF) at x.

                                                                                                                                                                                                                                                                                                                                    func (InverseGamma) Variance

                                                                                                                                                                                                                                                                                                                                    func (g InverseGamma) Variance() float64

                                                                                                                                                                                                                                                                                                                                      Variance returns the variance of the probability distribution.

                                                                                                                                                                                                                                                                                                                                      type KullbackLeibler

                                                                                                                                                                                                                                                                                                                                      type KullbackLeibler struct{}

                                                                                                                                                                                                                                                                                                                                        KullbackLeibler is a type for computing the Kullback-Leibler divergence from l to r.

                                                                                                                                                                                                                                                                                                                                        The Kullback-Leibler divergence is defined as

                                                                                                                                                                                                                                                                                                                                        D_KL(l || r ) = \int_x p(x) log(p(x)/q(x)) dx
                                                                                                                                                                                                                                                                                                                                        

                                                                                                                                                                                                                                                                                                                                        Note that the Kullback-Leibler divergence is not symmetric with respect to the order of the input arguments.

                                                                                                                                                                                                                                                                                                                                        func (KullbackLeibler) DistBeta

                                                                                                                                                                                                                                                                                                                                        func (KullbackLeibler) DistBeta(l, r Beta) float64

                                                                                                                                                                                                                                                                                                                                          DistBeta returns the Kullback-Leibler divergence between Beta distributions l and r.

                                                                                                                                                                                                                                                                                                                                          For two Beta distributions, the KL divergence is computed as

                                                                                                                                                                                                                                                                                                                                          D_KL(l || r) =  log Γ(α_l+β_l) - log Γ(α_l) - log Γ(β_l)
                                                                                                                                                                                                                                                                                                                                                          - log Γ(α_r+β_r) + log Γ(α_r) + log Γ(β_r)
                                                                                                                                                                                                                                                                                                                                                          + (α_l-α_r)(ψ(α_l)-ψ(α_l+β_l)) + (β_l-β_r)(ψ(β_l)-ψ(α_l+β_l))
                                                                                                                                                                                                                                                                                                                                          

                                                                                                                                                                                                                                                                                                                                          Where Γ is the gamma function and ψ is the digamma function.

                                                                                                                                                                                                                                                                                                                                          func (KullbackLeibler) DistNormal

                                                                                                                                                                                                                                                                                                                                          func (KullbackLeibler) DistNormal(l, r Normal) float64

                                                                                                                                                                                                                                                                                                                                            DistNormal returns the Kullback-Leibler divergence between Normal distributions l and r.

                                                                                                                                                                                                                                                                                                                                            For two Normal distributions, the KL divergence is computed as

                                                                                                                                                                                                                                                                                                                                            D_KL(l || r) = log(σ_r / σ_l) + (σ_l^2 + (μ_l-μ_r)^2)/(2 * σ_r^2) - 0.5
                                                                                                                                                                                                                                                                                                                                            

                                                                                                                                                                                                                                                                                                                                            type Laplace

                                                                                                                                                                                                                                                                                                                                            type Laplace struct {
                                                                                                                                                                                                                                                                                                                                            	Mu    float64 // Mean of the Laplace distribution
                                                                                                                                                                                                                                                                                                                                            	Scale float64 // Scale of the Laplace distribution
                                                                                                                                                                                                                                                                                                                                            	Src   rand.Source
                                                                                                                                                                                                                                                                                                                                            }

                                                                                                                                                                                                                                                                                                                                              Laplace represents the Laplace distribution (https://en.wikipedia.org/wiki/Laplace_distribution).

                                                                                                                                                                                                                                                                                                                                              func (Laplace) CDF

                                                                                                                                                                                                                                                                                                                                              func (l Laplace) CDF(x float64) float64

                                                                                                                                                                                                                                                                                                                                                CDF computes the value of the cumulative density function at x.

                                                                                                                                                                                                                                                                                                                                                func (Laplace) Entropy

                                                                                                                                                                                                                                                                                                                                                func (l Laplace) Entropy() float64

                                                                                                                                                                                                                                                                                                                                                  Entropy returns the entropy of the distribution.

                                                                                                                                                                                                                                                                                                                                                  func (Laplace) ExKurtosis

                                                                                                                                                                                                                                                                                                                                                  func (l Laplace) ExKurtosis() float64

                                                                                                                                                                                                                                                                                                                                                    ExKurtosis returns the excess kurtosis of the distribution.

                                                                                                                                                                                                                                                                                                                                                    func (*Laplace) Fit

                                                                                                                                                                                                                                                                                                                                                    func (l *Laplace) Fit(samples, weights []float64)

                                                                                                                                                                                                                                                                                                                                                      Fit sets the parameters of the probability distribution from the data samples x with relative weights w. If weights is nil, then all the weights are 1. If weights is not nil, then the len(weights) must equal len(samples).

                                                                                                                                                                                                                                                                                                                                                      Note: Laplace distribution has no FitPrior because it has no sufficient statistics.

                                                                                                                                                                                                                                                                                                                                                      func (Laplace) LogProb

                                                                                                                                                                                                                                                                                                                                                      func (l Laplace) LogProb(x float64) float64

                                                                                                                                                                                                                                                                                                                                                        LogProb computes the natural logarithm of the value of the probability density function at x.

                                                                                                                                                                                                                                                                                                                                                        func (Laplace) Mean

                                                                                                                                                                                                                                                                                                                                                        func (l Laplace) Mean() float64

                                                                                                                                                                                                                                                                                                                                                          Mean returns the mean of the probability distribution.

                                                                                                                                                                                                                                                                                                                                                          func (Laplace) Median

                                                                                                                                                                                                                                                                                                                                                          func (l Laplace) Median() float64

                                                                                                                                                                                                                                                                                                                                                            Median returns the median of the LaPlace distribution.

                                                                                                                                                                                                                                                                                                                                                            func (Laplace) Mode

                                                                                                                                                                                                                                                                                                                                                            func (l Laplace) Mode() float64

                                                                                                                                                                                                                                                                                                                                                              Mode returns the mode of the LaPlace distribution.

                                                                                                                                                                                                                                                                                                                                                              func (Laplace) NumParameters

                                                                                                                                                                                                                                                                                                                                                              func (l Laplace) NumParameters() int

                                                                                                                                                                                                                                                                                                                                                                NumParameters returns the number of parameters in the distribution.

                                                                                                                                                                                                                                                                                                                                                                func (Laplace) Prob

                                                                                                                                                                                                                                                                                                                                                                func (l Laplace) Prob(x float64) float64

                                                                                                                                                                                                                                                                                                                                                                  Prob computes the value of the probability density function at x.

                                                                                                                                                                                                                                                                                                                                                                  func (Laplace) Quantile

                                                                                                                                                                                                                                                                                                                                                                  func (l Laplace) Quantile(p float64) float64

                                                                                                                                                                                                                                                                                                                                                                    Quantile returns the inverse of the cumulative probability distribution.

                                                                                                                                                                                                                                                                                                                                                                    func (Laplace) Rand

                                                                                                                                                                                                                                                                                                                                                                    func (l Laplace) Rand() float64

                                                                                                                                                                                                                                                                                                                                                                      Rand returns a random sample drawn from the distribution.

                                                                                                                                                                                                                                                                                                                                                                      func (Laplace) Score

                                                                                                                                                                                                                                                                                                                                                                      func (l Laplace) Score(deriv []float64, x float64) []float64

                                                                                                                                                                                                                                                                                                                                                                        Score returns the score function with respect to the parameters of the distribution at the input location x. The score function is the derivative of the log-likelihood at x with respect to the parameters

                                                                                                                                                                                                                                                                                                                                                                        (∂/∂θ) log(p(x;θ))
                                                                                                                                                                                                                                                                                                                                                                        

                                                                                                                                                                                                                                                                                                                                                                        If deriv is non-nil, len(deriv) must equal the number of parameters otherwise Score will panic, and the derivative is stored in-place into deriv. If deriv is nil a new slice will be allocated and returned.

                                                                                                                                                                                                                                                                                                                                                                        The order is [∂LogProb / ∂Mu, ∂LogProb / ∂Scale].

                                                                                                                                                                                                                                                                                                                                                                        For more information, see https://en.wikipedia.org/wiki/Score_%28statistics%29.

                                                                                                                                                                                                                                                                                                                                                                        Special cases:

                                                                                                                                                                                                                                                                                                                                                                        Score(l.Mu) = [NaN, -1/l.Scale]
                                                                                                                                                                                                                                                                                                                                                                        

                                                                                                                                                                                                                                                                                                                                                                        func (Laplace) ScoreInput

                                                                                                                                                                                                                                                                                                                                                                        func (l Laplace) ScoreInput(x float64) float64

                                                                                                                                                                                                                                                                                                                                                                          ScoreInput returns the score function with respect to the input of the distribution at the input location specified by x. The score function is the derivative of the log-likelihood

                                                                                                                                                                                                                                                                                                                                                                          (d/dx) log(p(x)) .
                                                                                                                                                                                                                                                                                                                                                                          

                                                                                                                                                                                                                                                                                                                                                                          Special cases:

                                                                                                                                                                                                                                                                                                                                                                          ScoreInput(l.Mu) = NaN
                                                                                                                                                                                                                                                                                                                                                                          

                                                                                                                                                                                                                                                                                                                                                                          func (Laplace) Skewness

                                                                                                                                                                                                                                                                                                                                                                          func (Laplace) Skewness() float64

                                                                                                                                                                                                                                                                                                                                                                            Skewness returns the skewness of the distribution.

                                                                                                                                                                                                                                                                                                                                                                            func (Laplace) StdDev

                                                                                                                                                                                                                                                                                                                                                                            func (l Laplace) StdDev() float64

                                                                                                                                                                                                                                                                                                                                                                              StdDev returns the standard deviation of the distribution.

                                                                                                                                                                                                                                                                                                                                                                              func (Laplace) Survival

                                                                                                                                                                                                                                                                                                                                                                              func (l Laplace) Survival(x float64) float64

                                                                                                                                                                                                                                                                                                                                                                                Survival returns the survival function (complementary CDF) at x.

                                                                                                                                                                                                                                                                                                                                                                                func (Laplace) Variance

                                                                                                                                                                                                                                                                                                                                                                                func (l Laplace) Variance() float64

                                                                                                                                                                                                                                                                                                                                                                                  Variance returns the variance of the probability distribution.

                                                                                                                                                                                                                                                                                                                                                                                  type LogNormal

                                                                                                                                                                                                                                                                                                                                                                                  type LogNormal struct {
                                                                                                                                                                                                                                                                                                                                                                                  	Mu    float64
                                                                                                                                                                                                                                                                                                                                                                                  	Sigma float64
                                                                                                                                                                                                                                                                                                                                                                                  	Src   rand.Source
                                                                                                                                                                                                                                                                                                                                                                                  }

                                                                                                                                                                                                                                                                                                                                                                                    LogNormal represents a random variable whose log is normally distributed. The probability density function is given by

                                                                                                                                                                                                                                                                                                                                                                                    1/(x σ √2π) exp(-(ln(x)-μ)^2)/(2σ^2))
                                                                                                                                                                                                                                                                                                                                                                                    

                                                                                                                                                                                                                                                                                                                                                                                    func (LogNormal) CDF

                                                                                                                                                                                                                                                                                                                                                                                    func (l LogNormal) CDF(x float64) float64

                                                                                                                                                                                                                                                                                                                                                                                      CDF computes the value of the cumulative density function at x.

                                                                                                                                                                                                                                                                                                                                                                                      func (LogNormal) Entropy

                                                                                                                                                                                                                                                                                                                                                                                      func (l LogNormal) Entropy() float64

                                                                                                                                                                                                                                                                                                                                                                                        Entropy returns the differential entropy of the distribution.

                                                                                                                                                                                                                                                                                                                                                                                        func (LogNormal) ExKurtosis

                                                                                                                                                                                                                                                                                                                                                                                        func (l LogNormal) ExKurtosis() float64

                                                                                                                                                                                                                                                                                                                                                                                          ExKurtosis returns the excess kurtosis of the distribution.

                                                                                                                                                                                                                                                                                                                                                                                          func (LogNormal) LogProb

                                                                                                                                                                                                                                                                                                                                                                                          func (l LogNormal) LogProb(x float64) float64

                                                                                                                                                                                                                                                                                                                                                                                            LogProb computes the natural logarithm of the value of the probability density function at x.

                                                                                                                                                                                                                                                                                                                                                                                            func (LogNormal) Mean

                                                                                                                                                                                                                                                                                                                                                                                            func (l LogNormal) Mean() float64

                                                                                                                                                                                                                                                                                                                                                                                              Mean returns the mean of the probability distribution.

                                                                                                                                                                                                                                                                                                                                                                                              func (LogNormal) Median

                                                                                                                                                                                                                                                                                                                                                                                              func (l LogNormal) Median() float64

                                                                                                                                                                                                                                                                                                                                                                                                Median returns the median of the probability distribution.

                                                                                                                                                                                                                                                                                                                                                                                                func (LogNormal) Mode

                                                                                                                                                                                                                                                                                                                                                                                                func (l LogNormal) Mode() float64

                                                                                                                                                                                                                                                                                                                                                                                                  Mode returns the mode of the probability distribution.

                                                                                                                                                                                                                                                                                                                                                                                                  func (LogNormal) NumParameters

                                                                                                                                                                                                                                                                                                                                                                                                  func (LogNormal) NumParameters() int

                                                                                                                                                                                                                                                                                                                                                                                                    NumParameters returns the number of parameters in the distribution.

                                                                                                                                                                                                                                                                                                                                                                                                    func (LogNormal) Prob

                                                                                                                                                                                                                                                                                                                                                                                                    func (l LogNormal) Prob(x float64) float64

                                                                                                                                                                                                                                                                                                                                                                                                      Prob computes the value of the probability density function at x.

                                                                                                                                                                                                                                                                                                                                                                                                      func (LogNormal) Quantile

                                                                                                                                                                                                                                                                                                                                                                                                      func (l LogNormal) Quantile(p float64) float64

                                                                                                                                                                                                                                                                                                                                                                                                        Quantile returns the inverse of the cumulative probability distribution.

                                                                                                                                                                                                                                                                                                                                                                                                        func (LogNormal) Rand

                                                                                                                                                                                                                                                                                                                                                                                                        func (l LogNormal) Rand() float64

                                                                                                                                                                                                                                                                                                                                                                                                          Rand returns a random sample drawn from the distribution.

                                                                                                                                                                                                                                                                                                                                                                                                          func (LogNormal) Skewness

                                                                                                                                                                                                                                                                                                                                                                                                          func (l LogNormal) Skewness() float64

                                                                                                                                                                                                                                                                                                                                                                                                            Skewness returns the skewness of the distribution.

                                                                                                                                                                                                                                                                                                                                                                                                            func (LogNormal) StdDev

                                                                                                                                                                                                                                                                                                                                                                                                            func (l LogNormal) StdDev() float64

                                                                                                                                                                                                                                                                                                                                                                                                              StdDev returns the standard deviation of the probability distribution.

                                                                                                                                                                                                                                                                                                                                                                                                              func (LogNormal) Survival

                                                                                                                                                                                                                                                                                                                                                                                                              func (l LogNormal) Survival(x float64) float64

                                                                                                                                                                                                                                                                                                                                                                                                                Survival returns the survival function (complementary CDF) at x.

                                                                                                                                                                                                                                                                                                                                                                                                                func (LogNormal) Variance

                                                                                                                                                                                                                                                                                                                                                                                                                func (l LogNormal) Variance() float64

                                                                                                                                                                                                                                                                                                                                                                                                                  Variance returns the variance of the probability distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                  type LogProber

                                                                                                                                                                                                                                                                                                                                                                                                                  type LogProber interface {
                                                                                                                                                                                                                                                                                                                                                                                                                  	// LogProb returns the natural logarithm of the
                                                                                                                                                                                                                                                                                                                                                                                                                  	// value of the probability density or probability
                                                                                                                                                                                                                                                                                                                                                                                                                  	// mass function at x.
                                                                                                                                                                                                                                                                                                                                                                                                                  	LogProb(x float64) float64
                                                                                                                                                                                                                                                                                                                                                                                                                  }

                                                                                                                                                                                                                                                                                                                                                                                                                    LogProber wraps the LogProb method.

                                                                                                                                                                                                                                                                                                                                                                                                                    type Normal

                                                                                                                                                                                                                                                                                                                                                                                                                    type Normal struct {
                                                                                                                                                                                                                                                                                                                                                                                                                    	Mu    float64 // Mean of the normal distribution
                                                                                                                                                                                                                                                                                                                                                                                                                    	Sigma float64 // Standard deviation of the normal distribution
                                                                                                                                                                                                                                                                                                                                                                                                                    	Src   rand.Source
                                                                                                                                                                                                                                                                                                                                                                                                                    }

                                                                                                                                                                                                                                                                                                                                                                                                                      Normal respresents a normal (Gaussian) distribution (https://en.wikipedia.org/wiki/Normal_distribution).

                                                                                                                                                                                                                                                                                                                                                                                                                      Example
                                                                                                                                                                                                                                                                                                                                                                                                                      Output:
                                                                                                                                                                                                                                                                                                                                                                                                                      
                                                                                                                                                                                                                                                                                                                                                                                                                      mean= 2.0 ± 0.02
                                                                                                                                                                                                                                                                                                                                                                                                                      

                                                                                                                                                                                                                                                                                                                                                                                                                      func (Normal) CDF

                                                                                                                                                                                                                                                                                                                                                                                                                      func (n Normal) CDF(x float64) float64

                                                                                                                                                                                                                                                                                                                                                                                                                        CDF computes the value of the cumulative density function at x.

                                                                                                                                                                                                                                                                                                                                                                                                                        func (*Normal) ConjugateUpdate

                                                                                                                                                                                                                                                                                                                                                                                                                        func (n *Normal) ConjugateUpdate(suffStat []float64, nSamples float64, priorStrength []float64)

                                                                                                                                                                                                                                                                                                                                                                                                                          ConjugateUpdate updates the parameters of the distribution from the sufficient statistics of a set of samples. The sufficient statistics, suffStat, have been observed with nSamples observations. The prior values of the distribution are those currently in the distribution, and have been observed with priorStrength samples.

                                                                                                                                                                                                                                                                                                                                                                                                                          For the normal distribution, the sufficient statistics are the mean and uncorrected standard deviation of the samples. The prior is having seen strength[0] samples with mean Normal.Mu and strength[1] samples with standard deviation Normal.Sigma. As a result of this function, Normal.Mu and Normal.Sigma are updated based on the weighted samples, and strength is modified to include the new number of samples observed.

                                                                                                                                                                                                                                                                                                                                                                                                                          This function panics if len(suffStat) != n.NumSuffStat() or len(priorStrength) != n.NumSuffStat().

                                                                                                                                                                                                                                                                                                                                                                                                                          func (Normal) Entropy

                                                                                                                                                                                                                                                                                                                                                                                                                          func (n Normal) Entropy() float64

                                                                                                                                                                                                                                                                                                                                                                                                                            Entropy returns the differential entropy of the distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                            func (Normal) ExKurtosis

                                                                                                                                                                                                                                                                                                                                                                                                                            func (Normal) ExKurtosis() float64

                                                                                                                                                                                                                                                                                                                                                                                                                              ExKurtosis returns the excess kurtosis of the distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                              func (*Normal) Fit

                                                                                                                                                                                                                                                                                                                                                                                                                              func (n *Normal) Fit(samples, weights []float64)

                                                                                                                                                                                                                                                                                                                                                                                                                                Fit sets the parameters of the probability distribution from the data samples x with relative weights w. If weights is nil, then all the weights are 1. If weights is not nil, then the len(weights) must equal len(samples).

                                                                                                                                                                                                                                                                                                                                                                                                                                func (Normal) LogProb

                                                                                                                                                                                                                                                                                                                                                                                                                                func (n Normal) LogProb(x float64) float64

                                                                                                                                                                                                                                                                                                                                                                                                                                  LogProb computes the natural logarithm of the value of the probability density function at x.

                                                                                                                                                                                                                                                                                                                                                                                                                                  func (Normal) Mean

                                                                                                                                                                                                                                                                                                                                                                                                                                  func (n Normal) Mean() float64

                                                                                                                                                                                                                                                                                                                                                                                                                                    Mean returns the mean of the probability distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                    func (Normal) Median

                                                                                                                                                                                                                                                                                                                                                                                                                                    func (n Normal) Median() float64

                                                                                                                                                                                                                                                                                                                                                                                                                                      Median returns the median of the normal distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                      func (Normal) Mode

                                                                                                                                                                                                                                                                                                                                                                                                                                      func (n Normal) Mode() float64

                                                                                                                                                                                                                                                                                                                                                                                                                                        Mode returns the mode of the normal distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                        func (Normal) NumParameters

                                                                                                                                                                                                                                                                                                                                                                                                                                        func (Normal) NumParameters() int

                                                                                                                                                                                                                                                                                                                                                                                                                                          NumParameters returns the number of parameters in the distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                          func (Normal) NumSuffStat

                                                                                                                                                                                                                                                                                                                                                                                                                                          func (Normal) NumSuffStat() int

                                                                                                                                                                                                                                                                                                                                                                                                                                            NumSuffStat returns the number of sufficient statistics for the distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                            func (Normal) Prob

                                                                                                                                                                                                                                                                                                                                                                                                                                            func (n Normal) Prob(x float64) float64

                                                                                                                                                                                                                                                                                                                                                                                                                                              Prob computes the value of the probability density function at x.

                                                                                                                                                                                                                                                                                                                                                                                                                                              func (Normal) Quantile

                                                                                                                                                                                                                                                                                                                                                                                                                                              func (n Normal) Quantile(p float64) float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                Quantile returns the inverse of the cumulative probability distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                func (Normal) Rand

                                                                                                                                                                                                                                                                                                                                                                                                                                                func (n Normal) Rand() float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                  Rand returns a random sample drawn from the distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                  func (Normal) Score

                                                                                                                                                                                                                                                                                                                                                                                                                                                  func (n Normal) Score(deriv []float64, x float64) []float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                    Score returns the score function with respect to the parameters of the distribution at the input location x. The score function is the derivative of the log-likelihood at x with respect to the parameters

                                                                                                                                                                                                                                                                                                                                                                                                                                                    (∂/∂θ) log(p(x;θ))
                                                                                                                                                                                                                                                                                                                                                                                                                                                    

                                                                                                                                                                                                                                                                                                                                                                                                                                                    If deriv is non-nil, len(deriv) must equal the number of parameters otherwise Score will panic, and the derivative is stored in-place into deriv. If deriv is nil a new slice will be allocated and returned.

                                                                                                                                                                                                                                                                                                                                                                                                                                                    The order is [∂LogProb / ∂Mu, ∂LogProb / ∂Sigma].

                                                                                                                                                                                                                                                                                                                                                                                                                                                    For more information, see https://en.wikipedia.org/wiki/Score_%28statistics%29.

                                                                                                                                                                                                                                                                                                                                                                                                                                                    func (Normal) ScoreInput

                                                                                                                                                                                                                                                                                                                                                                                                                                                    func (n Normal) ScoreInput(x float64) float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                      ScoreInput returns the score function with respect to the input of the distribution at the input location specified by x. The score function is the derivative of the log-likelihood

                                                                                                                                                                                                                                                                                                                                                                                                                                                      (d/dx) log(p(x)) .
                                                                                                                                                                                                                                                                                                                                                                                                                                                      

                                                                                                                                                                                                                                                                                                                                                                                                                                                      func (Normal) Skewness

                                                                                                                                                                                                                                                                                                                                                                                                                                                      func (Normal) Skewness() float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                        Skewness returns the skewness of the distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                        func (Normal) StdDev

                                                                                                                                                                                                                                                                                                                                                                                                                                                        func (n Normal) StdDev() float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                          StdDev returns the standard deviation of the probability distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                          func (Normal) SuffStat

                                                                                                                                                                                                                                                                                                                                                                                                                                                          func (Normal) SuffStat(suffStat, samples, weights []float64) (nSamples float64)

                                                                                                                                                                                                                                                                                                                                                                                                                                                            SuffStat computes the sufficient statistics of a set of samples to update the distribution. The sufficient statistics are stored in place, and the effective number of samples are returned.

                                                                                                                                                                                                                                                                                                                                                                                                                                                            The normal distribution has two sufficient statistics, the mean of the samples and the standard deviation of the samples.

                                                                                                                                                                                                                                                                                                                                                                                                                                                            If weights is nil, the weights are assumed to be 1, otherwise panics if len(samples) != len(weights). Panics if len(suffStat) != NumSuffStat().

                                                                                                                                                                                                                                                                                                                                                                                                                                                            func (Normal) Survival

                                                                                                                                                                                                                                                                                                                                                                                                                                                            func (n Normal) Survival(x float64) float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                              Survival returns the survival function (complementary CDF) at x.

                                                                                                                                                                                                                                                                                                                                                                                                                                                              func (Normal) Variance

                                                                                                                                                                                                                                                                                                                                                                                                                                                              func (n Normal) Variance() float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                Variance returns the variance of the probability distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                type Parameter

                                                                                                                                                                                                                                                                                                                                                                                                                                                                type Parameter struct {
                                                                                                                                                                                                                                                                                                                                                                                                                                                                	Name  string
                                                                                                                                                                                                                                                                                                                                                                                                                                                                	Value float64
                                                                                                                                                                                                                                                                                                                                                                                                                                                                }

                                                                                                                                                                                                                                                                                                                                                                                                                                                                  Parameter represents a parameter of a probability distribution

                                                                                                                                                                                                                                                                                                                                                                                                                                                                  type Pareto

                                                                                                                                                                                                                                                                                                                                                                                                                                                                  type Pareto struct {
                                                                                                                                                                                                                                                                                                                                                                                                                                                                  	// Xm is the scale parameter.
                                                                                                                                                                                                                                                                                                                                                                                                                                                                  	// Xm must be greater than 0.
                                                                                                                                                                                                                                                                                                                                                                                                                                                                  	Xm float64
                                                                                                                                                                                                                                                                                                                                                                                                                                                                  
                                                                                                                                                                                                                                                                                                                                                                                                                                                                  	// Alpha is the shape parameter.
                                                                                                                                                                                                                                                                                                                                                                                                                                                                  	// Alpha must be greater than 0.
                                                                                                                                                                                                                                                                                                                                                                                                                                                                  	Alpha float64
                                                                                                                                                                                                                                                                                                                                                                                                                                                                  
                                                                                                                                                                                                                                                                                                                                                                                                                                                                  	Src rand.Source
                                                                                                                                                                                                                                                                                                                                                                                                                                                                  }

                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Pareto implements the Pareto (Type I) distribution, a one parameter distribution with support above the scale parameter.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                    The density function is given by

                                                                                                                                                                                                                                                                                                                                                                                                                                                                    (α x_m^{α})/(x^{α+1}) for x >= x_m.
                                                                                                                                                                                                                                                                                                                                                                                                                                                                    

                                                                                                                                                                                                                                                                                                                                                                                                                                                                    For more information, see https://en.wikipedia.org/wiki/Pareto_distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                    func (Pareto) CDF

                                                                                                                                                                                                                                                                                                                                                                                                                                                                    func (p Pareto) CDF(x float64) float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                      CDF computes the value of the cumulative density function at x.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                      func (Pareto) Entropy

                                                                                                                                                                                                                                                                                                                                                                                                                                                                      func (p Pareto) Entropy() float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                        Entropy returns the differential entropy of the distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                        func (Pareto) ExKurtosis

                                                                                                                                                                                                                                                                                                                                                                                                                                                                        func (p Pareto) ExKurtosis() float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                          ExKurtosis returns the excess kurtosis of the distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                          func (Pareto) LogProb

                                                                                                                                                                                                                                                                                                                                                                                                                                                                          func (p Pareto) LogProb(x float64) float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                            LogProb computes the natural logarithm of the value of the probability density function at x.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                            func (Pareto) Mean

                                                                                                                                                                                                                                                                                                                                                                                                                                                                            func (p Pareto) Mean() float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                              Mean returns the mean of the probability distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                              func (Pareto) Median

                                                                                                                                                                                                                                                                                                                                                                                                                                                                              func (p Pareto) Median() float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                Median returns the median of the pareto distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                func (Pareto) Mode

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                func (p Pareto) Mode() float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  Mode returns the mode of the distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  func (Pareto) NumParameters

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  func (p Pareto) NumParameters() int

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    NumParameters returns the number of parameters in the distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    func (Pareto) Prob

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    func (p Pareto) Prob(x float64) float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      Prob computes the value of the probability density function at x.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      func (Pareto) Quantile

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      func (p Pareto) Quantile(prob float64) float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        Quantile returns the inverse of the cumulative probability distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        func (Pareto) Rand

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        func (p Pareto) Rand() float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          Rand returns a random sample drawn from the distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          func (Pareto) StdDev

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          func (p Pareto) StdDev() float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            StdDev returns the standard deviation of the probability distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            func (Pareto) Survival

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            func (p Pareto) Survival(x float64) float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              Survival returns the survival function (complementary CDF) at x.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              func (Pareto) Variance

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              func (p Pareto) Variance() float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                Variance returns the variance of the probability distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                type Poisson

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                type Poisson struct {
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                	// Lambda is the average number of events in an interval.
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                	// Lambda must be greater than 0.
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                	Lambda float64
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                	Src rand.Source
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                }

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  Poisson implements the Poisson distribution, a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval. The poisson distribution has density function:

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  f(k) = λ^k / k! e^(-λ)
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  For more information, see https://en.wikipedia.org/wiki/Poisson_distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  func (Poisson) CDF

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  func (p Poisson) CDF(x float64) float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    CDF computes the value of the cumulative distribution function at x.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    func (Poisson) ExKurtosis

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    func (p Poisson) ExKurtosis() float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ExKurtosis returns the excess kurtosis of the distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      func (Poisson) LogProb

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      func (p Poisson) LogProb(x float64) float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        LogProb computes the natural logarithm of the value of the probability density function at x.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        func (Poisson) Mean

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        func (p Poisson) Mean() float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          Mean returns the mean of the probability distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          func (Poisson) NumParameters

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          func (Poisson) NumParameters() int

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            NumParameters returns the number of parameters in the distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            func (Poisson) Prob

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            func (p Poisson) Prob(x float64) float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              Prob computes the value of the probability density function at x.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              func (Poisson) Rand

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              func (p Poisson) Rand() float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                Rand returns a random sample drawn from the distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                func (Poisson) Skewness

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                func (p Poisson) Skewness() float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  Skewness returns the skewness of the distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  func (Poisson) StdDev

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  func (p Poisson) StdDev() float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    StdDev returns the standard deviation of the probability distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    func (Poisson) Survival

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    func (p Poisson) Survival(x float64) float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      Survival returns the survival function (complementary CDF) at x.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      func (Poisson) Variance

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      func (p Poisson) Variance() float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        Variance returns the variance of the probability distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        type Quantiler

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        type Quantiler interface {
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        	// Quantile returns the minimum value of x from amongst
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        	// all those values whose CDF value exceeds or equals p.
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        	Quantile(p float64) float64
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        }

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          Quantiler wraps the Quantile method.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          type RandLogProber

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          type RandLogProber interface {
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          	Rander
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          	LogProber
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          }

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            RandLogProber is the interface that groups the Rander and LogProber methods.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            type Rander

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            type Rander interface {
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            	// Rand returns a random sample drawn from the distribution.
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            	Rand() float64
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            }

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              Rander wraps the Rand method.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              type StudentsT

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              type StudentsT struct {
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              	// Mu is the location parameter of the distribution, and the mean of the
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              	// distribution
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              	Mu float64
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              	// Sigma is the scale parameter of the distribution. It is related to the
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              	// standard deviation by std = Sigma * sqrt(Nu/(Nu-2))
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              	Sigma float64
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              	// Nu is the shape prameter of the distribution, representing the number of
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              	// degrees of the distribution, and one less than the number of observations
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              	// from a Normal distribution.
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              	Nu float64
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              	Src rand.Source
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              }

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                StudentsT implements the three-parameter Student's T distribution, a distribution over the real numbers.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                The Student's T distribution has density function

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                Γ((ν+1)/2) / (sqrt(νπ) Γ(ν/2) σ) (1 + 1/ν * ((x-μ)/σ)^2)^(-(ν+1)/2)
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                The Student's T distribution approaches the normal distribution as ν → ∞.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                For more information, see https://en.wikipedia.org/wiki/Student%27s_t-distribution, specifically https://en.wikipedia.org/wiki/Student%27s_t-distribution#Non-standardized_Student.27s_t-distribution .

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                The standard Student's T distribution is with Mu = 0, and Sigma = 1.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                func (StudentsT) CDF

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                func (s StudentsT) CDF(x float64) float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  CDF computes the value of the cumulative distribution function at x.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  func (StudentsT) LogProb

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  func (s StudentsT) LogProb(x float64) float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    LogProb computes the natural logarithm of the value of the probability density function at x.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    func (StudentsT) Mean

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    func (s StudentsT) Mean() float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      Mean returns the mean of the probability distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      func (StudentsT) Mode

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      func (s StudentsT) Mode() float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        Mode returns the mode of the distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        func (StudentsT) NumParameters

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        func (StudentsT) NumParameters() int

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          NumParameters returns the number of parameters in the distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          func (StudentsT) Prob

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          func (s StudentsT) Prob(x float64) float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            Prob computes the value of the probability density function at x.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            func (StudentsT) Quantile

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            func (s StudentsT) Quantile(p float64) float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              Quantile returns the inverse of the cumulative distribution function.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              func (StudentsT) Rand

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              func (s StudentsT) Rand() float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                Rand returns a random sample drawn from the distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                func (StudentsT) StdDev

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                func (s StudentsT) StdDev() float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  StdDev returns the standard deviation of the probability distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  The standard deviation is undefined for ν <= 1, and this returns math.NaN().

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  func (StudentsT) Survival

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  func (s StudentsT) Survival(x float64) float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Survival returns the survival function (complementary CDF) at x.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    func (StudentsT) Variance

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    func (s StudentsT) Variance() float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      Variance returns the variance of the probability distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      The variance is undefined for ν <= 1, and this returns math.NaN().

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      type Triangle

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      type Triangle struct {
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      	// contains filtered or unexported fields
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      }

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        Triangle represents a triangle distribution (https://en.wikipedia.org/wiki/Triangular_distribution).

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        func NewTriangle

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        func NewTriangle(a, b, c float64, src rand.Source) Triangle

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          NewTriangle constructs a new triangle distribution with lower limit a, upper limit b, and mode c. Constraints are a < b and a ≤ c ≤ b. This distribution is uncommon in nature, but may be useful for simulation.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          func (Triangle) CDF

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          func (t Triangle) CDF(x float64) float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            CDF computes the value of the cumulative density function at x.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            func (Triangle) Entropy

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            func (t Triangle) Entropy() float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              Entropy returns the entropy of the distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              func (Triangle) ExKurtosis

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              func (Triangle) ExKurtosis() float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                ExKurtosis returns the excess kurtosis of the distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                func (Triangle) LogProb

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                func (t Triangle) LogProb(x float64) float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  LogProb computes the natural logarithm of the value of the probability density function at x.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  func (Triangle) Mean

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  func (t Triangle) Mean() float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Mean returns the mean of the probability distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    func (Triangle) Median

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    func (t Triangle) Median() float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      Median returns the median of the probability distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      func (Triangle) Mode

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      func (t Triangle) Mode() float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        Mode returns the mode of the probability distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        func (Triangle) NumParameters

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        func (Triangle) NumParameters() int

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          NumParameters returns the number of parameters in the distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          func (Triangle) Prob

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          func (t Triangle) Prob(x float64) float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            Prob computes the value of the probability density function at x.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            func (Triangle) Quantile

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            func (t Triangle) Quantile(p float64) float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              Quantile returns the inverse of the cumulative probability distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              func (Triangle) Rand

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              func (t Triangle) Rand() float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                Rand returns a random sample drawn from the distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                func (Triangle) Score

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                func (t Triangle) Score(deriv []float64, x float64) []float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  Score returns the score function with respect to the parameters of the distribution at the input location x. The score function is the derivative of the log-likelihood at x with respect to the parameters

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  (∂/∂θ) log(p(x;θ))
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  If deriv is non-nil, len(deriv) must equal the number of parameters otherwise Score will panic, and the derivative is stored in-place into deriv. If deriv is nil a new slice will be allocated and returned.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  The order is [∂LogProb / ∂Mu, ∂LogProb / ∂Sigma].

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  For more information, see https://en.wikipedia.org/wiki/Score_%28statistics%29.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  func (Triangle) ScoreInput

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  func (t Triangle) ScoreInput(x float64) float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ScoreInput returns the score function with respect to the input of the distribution at the input location specified by x. The score function is the derivative of the log-likelihood

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    (d/dx) log(p(x)) .
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Special cases (c is the mode of the distribution):

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ScoreInput(c) = NaN
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ScoreInput(x) = NaN for x not in (a, b)
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    func (Triangle) Skewness

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    func (t Triangle) Skewness() float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      Skewness returns the skewness of the distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      func (Triangle) StdDev

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      func (t Triangle) StdDev() float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        StdDev returns the standard deviation of the probability distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        func (Triangle) Survival

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        func (t Triangle) Survival(x float64) float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          Survival returns the survival function (complementary CDF) at x.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          func (Triangle) Variance

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          func (t Triangle) Variance() float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            Variance returns the variance of the probability distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            type Uniform

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            type Uniform struct {
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            	Min float64
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            	Max float64
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            	Src rand.Source
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            }

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              Uniform represents a continuous uniform distribution (https://en.wikipedia.org/wiki/Uniform_distribution_%28continuous%29).

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              func (Uniform) CDF

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              func (u Uniform) CDF(x float64) float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                CDF computes the value of the cumulative density function at x.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                func (Uniform) Entropy

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                func (u Uniform) Entropy() float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  Entropy returns the entropy of the distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  func (Uniform) ExKurtosis

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  func (Uniform) ExKurtosis() float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    ExKurtosis returns the excess kurtosis of the distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    func (Uniform) LogProb

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    func (u Uniform) LogProb(x float64) float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      LogProb computes the natural logarithm of the value of the probability density function at x.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      func (Uniform) Mean

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      func (u Uniform) Mean() float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        Mean returns the mean of the probability distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        func (Uniform) Median

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        func (u Uniform) Median() float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          Median returns the median of the probability distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          func (Uniform) NumParameters

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          func (Uniform) NumParameters() int

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            NumParameters returns the number of parameters in the distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            func (Uniform) Prob

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            func (u Uniform) Prob(x float64) float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              Prob computes the value of the probability density function at x.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              func (Uniform) Quantile

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              func (u Uniform) Quantile(p float64) float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                Quantile returns the inverse of the cumulative probability distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                func (Uniform) Rand

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                func (u Uniform) Rand() float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  Rand returns a random sample drawn from the distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  func (Uniform) Score

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  func (u Uniform) Score(deriv []float64, x float64) []float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Score returns the score function with respect to the parameters of the distribution at the input location x. The score function is the derivative of the log-likelihood at x with respect to the parameters

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    (∂/∂θ) log(p(x;θ))
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    If deriv is non-nil, len(deriv) must equal the number of parameters otherwise Score will panic, and the derivative is stored in-place into deriv. If deriv is nil a new slice will be allocated and returned.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    The order is [∂LogProb / ∂Mu, ∂LogProb / ∂Sigma].

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    For more information, see https://en.wikipedia.org/wiki/Score_%28statistics%29.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    func (Uniform) ScoreInput

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    func (u Uniform) ScoreInput(x float64) float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ScoreInput returns the score function with respect to the input of the distribution at the input location specified by x. The score function is the derivative of the log-likelihood

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      (d/dx) log(p(x)) .
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      func (Uniform) Skewness

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      func (Uniform) Skewness() float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        Skewness returns the skewness of the distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        func (Uniform) StdDev

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        func (u Uniform) StdDev() float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          StdDev returns the standard deviation of the probability distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          func (Uniform) Survival

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          func (u Uniform) Survival(x float64) float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            Survival returns the survival function (complementary CDF) at x.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            func (Uniform) Variance

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            func (u Uniform) Variance() float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              Variance returns the variance of the probability distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              type Weibull

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              type Weibull struct {
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              	// Shape parameter of the distribution. A value of 1 represents
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              	// the exponential distribution. A value of 2 represents the
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              	// Rayleigh distribution. Valid range is (0,+∞).
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              	K float64
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              	// Scale parameter of the distribution. Valid range is (0,+∞).
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              	Lambda float64
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              	// Source of random numbers
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              	Src rand.Source
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              }

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                Weibull distribution. Valid range for x is [0,+∞).

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                func (Weibull) CDF

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                func (w Weibull) CDF(x float64) float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  CDF computes the value of the cumulative density function at x.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  func (Weibull) Entropy

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  func (w Weibull) Entropy() float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Entropy returns the entropy of the distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    func (Weibull) ExKurtosis

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    func (w Weibull) ExKurtosis() float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      ExKurtosis returns the excess kurtosis of the distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      func (Weibull) LogProb

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      func (w Weibull) LogProb(x float64) float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        LogProb computes the natural logarithm of the value of the probability density function at x. -Inf is returned if x is less than zero.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        Special cases occur when x == 0, and the result depends on the shape parameter as follows:

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        If 0 < K < 1, LogProb returns +Inf.
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        If K == 1, LogProb returns 0.
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        If K > 1, LogProb returns -Inf.
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        func (Weibull) LogSurvival

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        func (w Weibull) LogSurvival(x float64) float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          LogSurvival returns the log of the survival function (complementary CDF) at x.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          func (Weibull) Mean

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          func (w Weibull) Mean() float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            Mean returns the mean of the probability distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            func (Weibull) Median

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            func (w Weibull) Median() float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              Median returns the median of the normal distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              func (Weibull) Mode

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              func (w Weibull) Mode() float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                Mode returns the mode of the normal distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                The mode is NaN in the special case where the K (shape) parameter is less than 1.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                func (Weibull) NumParameters

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                func (Weibull) NumParameters() int

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  NumParameters returns the number of parameters in the distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  func (Weibull) Prob

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  func (w Weibull) Prob(x float64) float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Prob computes the value of the probability density function at x.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    func (Weibull) Quantile

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    func (w Weibull) Quantile(p float64) float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      Quantile returns the inverse of the cumulative probability distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      func (Weibull) Rand

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      func (w Weibull) Rand() float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        Rand returns a random sample drawn from the distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        func (Weibull) Score

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        func (w Weibull) Score(deriv []float64, x float64) []float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          Score returns the score function with respect to the parameters of the distribution at the input location x. The score function is the derivative of the log-likelihood at x with respect to the parameters

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          (∂/∂θ) log(p(x;θ))
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          If deriv is non-nil, len(deriv) must equal the number of parameters otherwise Score will panic, and the derivative is stored in-place into deriv. If deriv is nil a new slice will be allocated and returned.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          The order is [∂LogProb / ∂K, ∂LogProb / ∂λ].

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          For more information, see https://en.wikipedia.org/wiki/Score_%28statistics%29.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          Special cases:

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          Score(x) = [NaN, NaN] for x <= 0
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          func (Weibull) ScoreInput

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          func (w Weibull) ScoreInput(x float64) float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ScoreInput returns the score function with respect to the input of the distribution at the input location specified by x. The score function is the derivative of the log-likelihood

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            (d/dx) log(p(x)) .
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            Special cases:

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ScoreInput(x) = NaN for x <= 0
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            func (Weibull) Skewness

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            func (w Weibull) Skewness() float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              Skewness returns the skewness of the distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              func (Weibull) StdDev

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              func (w Weibull) StdDev() float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                StdDev returns the standard deviation of the probability distribution.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                func (Weibull) Survival

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                func (w Weibull) Survival(x float64) float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  Survival returns the survival function (complementary CDF) at x.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  func (Weibull) Variance

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  func (w Weibull) Variance() float64

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Variance returns the variance of the probability distribution.