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 // Copyright ©2016 The Gonum Authors. All rights reserved. // Use of this source code is governed by a BSD-style // license that can be found in the LICENSE file. package distuv import ( "math" "golang.org/x/exp/rand" "gonum.org/v1/gonum/mathext" ) // 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. type ChiSquared struct { // K is the shape parameter, corresponding to the degrees of freedom. Must // be greater than 0. K float64 Src rand.Source } // CDF computes the value of the cumulative density function at x. func (c ChiSquared) CDF(x float64) float64 { return mathext.GammaIncReg(c.K/2, x/2) } // ExKurtosis returns the excess kurtosis of the distribution. func (c ChiSquared) ExKurtosis() float64 { return 12 / c.K } // LogProb computes the natural logarithm of the value of the probability // density function at x. func (c ChiSquared) LogProb(x float64) float64 { if x < 0 { return math.Inf(-1) } lg, _ := math.Lgamma(c.K / 2) return (c.K/2-1)*math.Log(x) - x/2 - (c.K/2)*math.Ln2 - lg } // Mean returns the mean of the probability distribution. func (c ChiSquared) Mean() float64 { return c.K } // Mode returns the mode of the distribution. func (c ChiSquared) Mode() float64 { return math.Max(c.K-2, 0) } // NumParameters returns the number of parameters in the distribution. func (c ChiSquared) NumParameters() int { return 1 } // Prob computes the value of the probability density function at x. func (c ChiSquared) Prob(x float64) float64 { return math.Exp(c.LogProb(x)) } // Rand returns a random sample drawn from the distribution. func (c ChiSquared) Rand() float64 { return Gamma{c.K / 2, 0.5, c.Src}.Rand() } // Quantile returns the inverse of the cumulative distribution function. func (c ChiSquared) Quantile(p float64) float64 { if p < 0 || p > 1 { panic(badPercentile) } return mathext.GammaIncRegInv(0.5*c.K, p) * 2 } // StdDev returns the standard deviation of the probability distribution. func (c ChiSquared) StdDev() float64 { return math.Sqrt(c.Variance()) } // Survival returns the survival function (complementary CDF) at x. func (c ChiSquared) Survival(x float64) float64 { if x < 0 { return 1 } return mathext.GammaIncRegComp(0.5*c.K, 0.5*x) } // Variance returns the variance of the probability distribution. func (c ChiSquared) Variance() float64 { return 2 * c.K }