distuv

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 Go to latest Published: Dec 9, 2020 License: BSD-2-Clause Imports: 7 Imported by: 0

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 Bernoulli 

type Bernoulli struct {
	P      float64
	Source *rand.Rand
}

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 inverse of the cumulative probability distribution.

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

	Source *rand.Rand
}

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) 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 either parameter is less than or equal to 1 as a special case.

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 Categorical 

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

Categorical is an extension of the Bernouilli 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.Rand) 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.Rand
}

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
	Source *rand.Rand
}

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) != 1 or len(priorStrength) != 1.

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(samples, weights, suffStat []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
	Source *rand.Rand
}

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

	Source *rand.Rand
}

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 Laplace 

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

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) MarshalParameters 

func (l Laplace) MarshalParameters(p []Parameter)

MarshalParameters implements the ParameterMarshaler interface

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(0) = [0, -0.5/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) = 0

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) UnmarshalParameters 

func (l *Laplace) UnmarshalParameters(p []Parameter)

UnmarshalParameters implements the ParameterMarshaler interface

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
	Source *rand.Rand
}

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(float64) float64
}

type Normal 

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

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

Example 
package main

import (
	"fmt"

	"github.com/gonum/stat"
	"github.com/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) != 2 or len(priorStrength) != 2.

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(samples, weights, suffStat []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 Quantiler 

type Quantiler interface {
	Quantile(p float64) float64
}

type RandLogProber 

type RandLogProber interface {
	Rander
	LogProber
}

type Rander 

type Rander interface {
	Rand() float64
}

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.Rand
}

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 Uniform 

type Uniform struct {
	Min    float64
	Max    float64
	Source *rand.Rand
}

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) MarshalParameters 

func (u Uniform) MarshalParameters(p []Parameter)

MarshalParameters implements the ParameterMarshaler interface

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) 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) UnmarshalParameters 

func (u *Uniform) UnmarshalParameters(p []Parameter)

UnmarshalParameters implements the ParameterMarshaler interface

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
	Source *rand.Rand
}

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) LogCDF 

func (w Weibull) LogCDF(x float64) complex128

LogCDF computes the value of the log of the cumulative density function at x.

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. Zero 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

Survival 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(0) = [NaN, NaN]

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(0) = NaN

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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