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118 lines
3.2 KiB
Go
118 lines
3.2 KiB
Go
// Copyright ©2018 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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)
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// GumbelRight implements the right-skewed Gumbel distribution, a two-parameter
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// continuous distribution with support over the real numbers. The right-skewed
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// Gumbel distribution is also sometimes known as the Extreme Value distribution.
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//
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// The right-skewed Gumbel distribution has density function
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// 1/beta * exp(-(z + exp(-z)))
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// z = (x - mu)/beta
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// Beta must be greater than 0.
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//
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// For more information, see https://en.wikipedia.org/wiki/Gumbel_distribution.
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type GumbelRight struct {
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Mu float64
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Beta float64
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Src rand.Source
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}
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func (g GumbelRight) z(x float64) float64 {
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return (x - g.Mu) / g.Beta
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}
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// CDF computes the value of the cumulative density function at x.
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func (g GumbelRight) CDF(x float64) float64 {
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z := g.z(x)
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return math.Exp(-math.Exp(-z))
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}
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// Entropy returns the differential entropy of the distribution.
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func (g GumbelRight) Entropy() float64 {
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return math.Log(g.Beta) + eulerMascheroni + 1
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}
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// ExKurtosis returns the excess kurtosis of the distribution.
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func (g GumbelRight) ExKurtosis() float64 {
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return 12.0 / 5
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}
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// LogProb computes the natural logarithm of the value of the probability density function at x.
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func (g GumbelRight) LogProb(x float64) float64 {
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z := g.z(x)
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return -math.Log(g.Beta) - z - math.Exp(-z)
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}
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// Mean returns the mean of the probability distribution.
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func (g GumbelRight) Mean() float64 {
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return g.Mu + g.Beta*eulerMascheroni
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}
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// Median returns the median of the normal distribution.
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func (g GumbelRight) Median() float64 {
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return g.Mu - g.Beta*math.Log(math.Ln2)
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}
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// Mode returns the mode of the normal distribution.
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func (g GumbelRight) Mode() float64 {
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return g.Mu
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}
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// NumParameters returns the number of parameters in the distribution.
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func (GumbelRight) 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 (g GumbelRight) Prob(x float64) float64 {
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return math.Exp(g.LogProb(x))
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}
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// Quantile returns the inverse of the cumulative probability distribution.
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func (g GumbelRight) Quantile(p float64) float64 {
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if p < 0 || 1 < p {
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panic(badPercentile)
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}
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return g.Mu - g.Beta*math.Log(-math.Log(p))
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}
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// Rand returns a random sample drawn from the distribution.
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func (g GumbelRight) Rand() float64 {
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var rnd float64
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if g.Src == nil {
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rnd = rand.ExpFloat64()
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} else {
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rnd = rand.New(g.Src).ExpFloat64()
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}
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return g.Mu - g.Beta*math.Log(rnd)
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}
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// Skewness returns the skewness of the distribution.
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func (GumbelRight) Skewness() float64 {
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return 12 * math.Sqrt(6) * apery / (math.Pi * math.Pi * math.Pi)
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}
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// StdDev returns the standard deviation of the probability distribution.
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func (g GumbelRight) StdDev() float64 {
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return (math.Pi / math.Sqrt(6)) * g.Beta
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}
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// Survival returns the survival function (complementary CDF) at x.
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func (g GumbelRight) Survival(x float64) float64 {
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return 1 - g.CDF(x)
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}
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// Variance returns the variance of the probability distribution.
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func (g GumbelRight) Variance() float64 {
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return math.Pi * math.Pi * g.Beta * g.Beta / 6
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}
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