distuv

package
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 Go to latest Published: Apr 24, 2023 License: BSD-3-Clause Imports: 7 Imported by: 396

Documentation

Overview

Package distuv provides univariate random distribution types.

Index

Examples

Constants

This section is empty.

Variables

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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 added in v0.8.0 

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 added in v0.8.0 

func (a AlphaStable) ExKurtosis() float64

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

func (AlphaStable) Mean added in v0.8.0 

func (a AlphaStable) Mean() float64

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

func (AlphaStable) Median added in v0.8.0 

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 added in v0.8.0 

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 added in v0.8.0 

func (a AlphaStable) NumParameters() int

NumParameters returns the number of parameters in the distribution.

func (AlphaStable) Rand added in v0.8.0 

func (a AlphaStable) Rand() float64

Rand returns a random sample drawn from the distribution.

func (AlphaStable) Skewness added in v0.8.0 

func (a AlphaStable) Skewness() float64

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

func (AlphaStable) StdDev added in v0.8.0 

func (a AlphaStable) StdDev() float64

StdDev returns the standard deviation of the probability distribution.

func (AlphaStable) Variance added in v0.8.0 

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 parameters 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 Chi added in v0.11.0 

type Chi struct {
	// K is the shape parameter, corresponding to the degrees of freedom. Must
	// be greater than 0.
	K float64

	Src rand.Source
}

Chi implements the χ distribution, a one parameter distribution with support on the positive numbers.

The density function is given by 

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

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

func (Chi) CDF added in v0.11.0 

func (c Chi) CDF(x float64) float64

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

func (Chi) Entropy added in v0.11.0 

func (c Chi) Entropy() float64

Entropy returns the differential entropy of the distribution.

func (Chi) ExKurtosis added in v0.11.0 

func (c Chi) ExKurtosis() float64

ExKurtosis returns the excess kurtosis of the distribution.

func (Chi) LogProb added in v0.11.0 

func (c Chi) LogProb(x float64) float64

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

func (Chi) Mean added in v0.11.0 

func (c Chi) Mean() float64

Mean returns the mean of the probability distribution.

func (Chi) Median added in v0.11.0 

func (c Chi) Median() float64

Median returns the median of the distribution.

func (Chi) Mode added in v0.11.0 

func (c Chi) Mode() float64

Mode returns the mode of the distribution.

Mode returns NaN if K is less than one.

func (Chi) NumParameters added in v0.11.0 

func (c Chi) NumParameters() int

NumParameters returns the number of parameters in the distribution.

func (Chi) Prob added in v0.11.0 

func (c Chi) Prob(x float64) float64

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

func (Chi) Quantile added in v0.11.0 

func (c Chi) Quantile(p float64) float64

Quantile returns the inverse of the cumulative distribution function.

func (Chi) Rand added in v0.11.0 

func (c Chi) Rand() float64

Rand returns a random sample drawn from the distribution.

func (Chi) Skewness added in v0.11.0 

func (c Chi) Skewness() float64

Skewness returns the skewness of the distribution.

func (Chi) StdDev added in v0.11.0 

func (c Chi) StdDev() float64

StdDev returns the standard deviation of the probability distribution.

func (Chi) Survival added in v0.11.0 

func (c Chi) Survival(x float64) float64

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

func (Chi) Variance added in v0.11.0 

func (c Chi) Variance() float64

Variance returns the variance of the probability distribution.

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 Logistic added in v0.11.0 

type Logistic struct {
	Mu float64 // Mean value
	S  float64 // Scale parameter proportional to standard deviation
}

Logistic implements the Logistic distribution, a two-parameter distribution with support on the real axis. Its cumulative distribution function is the logistic function.

General form of probability density function for Logistic distribution is 

E(x) / (s * (1 + E(x))^2)
where E(x) = exp(-(x-μ)/s)

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

func (Logistic) CDF added in v0.11.0 

func (l Logistic) CDF(x float64) float64

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

func (Logistic) ExKurtosis added in v0.11.0 

func (l Logistic) ExKurtosis() float64

ExKurtosis returns the excess kurtosis of the distribution.

func (Logistic) LogProb added in v0.11.0 

func (l Logistic) LogProb(x float64) float64

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

func (Logistic) Mean added in v0.11.0 

func (l Logistic) Mean() float64

Mean returns the mean of the probability distribution.

func (Logistic) Median added in v0.11.0 

func (l Logistic) Median() float64

Median returns the median of the distribution.

It is same as Mean for Logistic distribution.

func (Logistic) Mode added in v0.11.0 

func (l Logistic) Mode() float64

Mode returns the mode of the distribution.

It is same as Mean for Logistic distribution.

func (Logistic) NumParameters added in v0.11.0 

func (l Logistic) NumParameters() int

NumParameters returns the number of parameters in the distribution.

Always returns 2.

func (Logistic) Prob added in v0.11.0 

func (l Logistic) Prob(x float64) float64

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

func (Logistic) Quantile added in v0.11.0 

func (l Logistic) Quantile(p float64) float64

Quantile returns the inverse of the cumulative distribution function.

func (Logistic) Skewness added in v0.11.0 

func (l Logistic) Skewness() float64

Skewness returns the skewness of the distribution.

Always 0 for Logistic distribution.

func (Logistic) StdDev added in v0.11.0 

func (l Logistic) StdDev() float64

StdDev returns the standard deviation of the probability distribution.

func (Logistic) Survival added in v0.11.0 

func (l Logistic) Survival(x float64) float64

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

func (Logistic) Variance added in v0.11.0 

func (l Logistic) Variance() float64

Variance returns the variance of the probability distribution.

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 
package main

import (
	"fmt"

	"gonum.org/v1/gonum/stat"
	"gonum.org/v1/gonum/stat/distuv"
)

func main() {
	// Create a normal distribution
	dist := distuv.Normal{
		Mu:    2,
		Sigma: 5,
	}

	data := make([]float64, 1e5)

	// Draw some random values from the standard normal distribution
	for i := range data {
		data[i] = dist.Rand()
	}

	mean, std := stat.MeanStdDev(data, nil)
	meanErr := stat.StdErr(std, float64(len(data)))

	fmt.Printf("mean= %1.1f ± %0.1v\n", mean, meanErr)

}

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 added in v0.8.0 

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 parameter 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 added in v0.8.0 

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 added in v0.8.0 

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 added in v0.8.0 

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 added in v0.8.0 

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.

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