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101 lines
2.6 KiB
Go
101 lines
2.6 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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// ChiSquared implements the χ² distribution, a one parameter distribution
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// with support on the positive numbers.
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//
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// The density function is given by
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// 1/(2^{k/2} * Γ(k/2)) * x^{k/2 - 1} * e^{-x/2}
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// It is a special case of the Gamma distribution, Γ(k/2, 1/2).
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//
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// For more information, see https://en.wikipedia.org/wiki/Chi-squared_distribution.
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type ChiSquared struct {
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// K is the shape parameter, corresponding to the degrees of freedom. Must
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// be greater than 0.
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K float64
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Src rand.Source
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}
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// CDF computes the value of the cumulative density function at x.
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func (c ChiSquared) CDF(x float64) float64 {
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return mathext.GammaInc(c.K/2, x/2)
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}
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// ExKurtosis returns the excess kurtosis of the distribution.
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func (c ChiSquared) ExKurtosis() float64 {
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return 12 / c.K
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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 (c ChiSquared) LogProb(x float64) float64 {
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if x < 0 {
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return math.Inf(-1)
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}
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lg, _ := math.Lgamma(c.K / 2)
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return (c.K/2-1)*math.Log(x) - x/2 - (c.K/2)*math.Ln2 - lg
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}
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// Mean returns the mean of the probability distribution.
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func (c ChiSquared) Mean() float64 {
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return c.K
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}
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// Mode returns the mode of the distribution.
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func (c ChiSquared) Mode() float64 {
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return math.Min(c.K-2, 0)
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}
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// NumParameters returns the number of parameters in the distribution.
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func (c ChiSquared) NumParameters() int {
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return 1
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}
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// Prob computes the value of the probability density function at x.
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func (c ChiSquared) Prob(x float64) float64 {
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return math.Exp(c.LogProb(x))
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}
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// Rand returns a random sample drawn from the distribution.
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func (c ChiSquared) Rand() float64 {
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return Gamma{c.K / 2, 0.5, c.Src}.Rand()
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}
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// Quantile returns the inverse of the cumulative distribution function.
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func (c ChiSquared) 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.GammaIncInv(0.5*c.K, p) * 2
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}
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// StdDev returns the standard deviation of the probability distribution.
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func (c ChiSquared) StdDev() float64 {
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return math.Sqrt(c.Variance())
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}
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// Survival returns the survival function (complementary CDF) at x.
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func (c ChiSquared) Survival(x float64) float64 {
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if x < 0 {
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return 1
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}
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return mathext.GammaIncComp(0.5*c.K, 0.5*x)
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}
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// Variance returns the variance of the probability distribution.
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func (c ChiSquared) Variance() float64 {
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return 2 * c.K
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}
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