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137 lines
3.7 KiB
Go
137 lines
3.7 KiB
Go
// Copyright ©2016 The Gonum Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package distuv
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import (
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"math"
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"golang.org/x/exp/rand"
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"gonum.org/v1/gonum/mathext"
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)
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// Beta implements the Beta distribution, a two-parameter continuous distribution
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// with support between 0 and 1.
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//
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// The beta distribution has density function
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// x^(α-1) * (1-x)^(β-1) * Γ(α+β) / (Γ(α)*Γ(β))
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//
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// For more information, see https://en.wikipedia.org/wiki/Beta_distribution
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type Beta struct {
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// Alpha is the left shape parameter of the distribution. Alpha must be greater
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// than 0.
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Alpha float64
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// Beta is the right shape parameter of the distribution. Beta must be greater
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// than 0.
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Beta float64
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Src rand.Source
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}
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// CDF computes the value of the cumulative distribution function at x.
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func (b Beta) CDF(x float64) float64 {
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if x <= 0 {
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return 0
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}
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if x >= 1 {
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return 1
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}
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return mathext.RegIncBeta(b.Alpha, b.Beta, x)
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}
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// Entropy returns the differential entropy of the distribution.
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func (b Beta) Entropy() float64 {
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if b.Alpha <= 0 || b.Beta <= 0 {
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panic("beta: negative parameters")
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}
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return mathext.Lbeta(b.Alpha, b.Beta) - (b.Alpha-1)*mathext.Digamma(b.Alpha) -
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(b.Beta-1)*mathext.Digamma(b.Beta) + (b.Alpha+b.Beta-2)*mathext.Digamma(b.Alpha+b.Beta)
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}
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// ExKurtosis returns the excess kurtosis of the distribution.
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func (b Beta) ExKurtosis() float64 {
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num := 6 * ((b.Alpha-b.Beta)*(b.Alpha-b.Beta)*(b.Alpha+b.Beta+1) - b.Alpha*b.Beta*(b.Alpha+b.Beta+2))
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den := b.Alpha * b.Beta * (b.Alpha + b.Beta + 2) * (b.Alpha + b.Beta + 3)
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return num / den
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}
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// LogProb computes the natural logarithm of the value of the probability
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// density function at x.
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func (b Beta) LogProb(x float64) float64 {
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if x < 0 || x > 1 {
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return math.Inf(-1)
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}
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if b.Alpha <= 0 || b.Beta <= 0 {
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panic("beta: negative parameters")
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}
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lab, _ := math.Lgamma(b.Alpha + b.Beta)
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la, _ := math.Lgamma(b.Alpha)
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lb, _ := math.Lgamma(b.Beta)
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return lab - la - lb + (b.Alpha-1)*math.Log(x) + (b.Beta-1)*math.Log(1-x)
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}
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// Mean returns the mean of the probability distribution.
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func (b Beta) Mean() float64 {
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return b.Alpha / (b.Alpha + b.Beta)
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}
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// Mode returns the mode of the distribution.
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//
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// Mode returns NaN if either parameter is less than or equal to 1 as a special case.
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func (b Beta) Mode() float64 {
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if b.Alpha <= 1 || b.Beta <= 1 {
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return math.NaN()
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}
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return (b.Alpha - 1) / (b.Alpha + b.Beta - 2)
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}
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// NumParameters returns the number of parameters in the distribution.
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func (b Beta) NumParameters() int {
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return 2
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}
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// Prob computes the value of the probability density function at x.
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func (b Beta) Prob(x float64) float64 {
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return math.Exp(b.LogProb(x))
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}
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// Quantile returns the inverse of the cumulative distribution function.
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func (b Beta) Quantile(p float64) float64 {
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if p < 0 || p > 1 {
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panic(badPercentile)
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}
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return mathext.InvRegIncBeta(b.Alpha, b.Beta, p)
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}
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// Rand returns a random sample drawn from the distribution.
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func (b Beta) Rand() float64 {
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ga := Gamma{Alpha: b.Alpha, Beta: 1, Src: b.Src}.Rand()
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gb := Gamma{Alpha: b.Beta, Beta: 1, Src: b.Src}.Rand()
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return ga / (ga + gb)
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}
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// StdDev returns the standard deviation of the probability distribution.
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func (b Beta) StdDev() float64 {
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return math.Sqrt(b.Variance())
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}
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// Survival returns the survival function (complementary CDF) at x.
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func (b Beta) Survival(x float64) float64 {
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switch {
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case x <= 0:
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return 1
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case x >= 1:
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return 0
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}
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return mathext.RegIncBeta(b.Beta, b.Alpha, 1-x)
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}
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// Variance returns the variance of the probability distribution.
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func (b Beta) Variance() float64 {
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return b.Alpha * b.Beta / ((b.Alpha + b.Beta) * (b.Alpha + b.Beta) * (b.Alpha + b.Beta + 1))
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}
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