fixed dependencies

vendor/gonum.org/v1/gonum/stat/distuv/chi.go

@@ -0,0 +1,125 @@
+// Copyright ©2021 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"
+)
+
+// Chi implements the χ distribution, a one parameter distribution
+// with support on the positive numbers.
+//
+// The density function is given by
+//
+//	1/(2^{k/2-1} * Γ(k/2)) * x^{k - 1} * e^{-x^2/2}
+//
+// For more information, see https://en.wikipedia.org/wiki/Chi_distribution.
+type Chi 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 Chi) CDF(x float64) float64 {
+	return mathext.GammaIncReg(c.K/2, (x*x)/2)
+}
+
+// Entropy returns the differential entropy of the distribution.
+func (c Chi) Entropy() float64 {
+	lg, _ := math.Lgamma(c.K / 2)
+	return lg + 0.5*(c.K-math.Ln2-(c.K-1)*mathext.Digamma(c.K/2))
+}
+
+// ExKurtosis returns the excess kurtosis of the distribution.
+func (c Chi) ExKurtosis() float64 {
+	v := c.Variance()
+	s := math.Sqrt(v)
+	return 2 / v * (1 - c.Mean()*s*c.Skewness() - v)
+}
+
+// LogProb computes the natural logarithm of the value of the probability
+// density function at x.
+func (c Chi) LogProb(x float64) float64 {
+	if x < 0 {
+		return math.Inf(-1)
+	}
+	lg, _ := math.Lgamma(c.K / 2)
+	return (c.K-1)*math.Log(x) - (x*x)/2 - (c.K/2-1)*math.Ln2 - lg
+}
+
+// Mean returns the mean of the probability distribution.
+func (c Chi) Mean() float64 {
+	lg1, _ := math.Lgamma((c.K + 1) / 2)
+	lg, _ := math.Lgamma(c.K / 2)
+	return math.Sqrt2 * math.Exp(lg1-lg)
+}
+
+// Median returns the median of the distribution.
+func (c Chi) Median() float64 {
+	return c.Quantile(0.5)
+}
+
+// Mode returns the mode of the distribution.
+//
+// Mode returns NaN if K is less than one.
+func (c Chi) Mode() float64 {
+	return math.Sqrt(c.K - 1)
+}
+
+// NumParameters returns the number of parameters in the distribution.
+func (c Chi) NumParameters() int {
+	return 1
+}
+
+// Prob computes the value of the probability density function at x.
+func (c Chi) Prob(x float64) float64 {
+	return math.Exp(c.LogProb(x))
+}
+
+// Rand returns a random sample drawn from the distribution.
+func (c Chi) Rand() float64 {
+	return math.Sqrt(Gamma{c.K / 2, 0.5, c.Src}.Rand())
+}
+
+// Quantile returns the inverse of the cumulative distribution function.
+func (c Chi) Quantile(p float64) float64 {
+	if p < 0 || 1 < p {
+		panic(badPercentile)
+	}
+	return math.Sqrt(2 * mathext.GammaIncRegInv(0.5*c.K, p))
+}
+
+// Skewness returns the skewness of the distribution.
+func (c Chi) Skewness() float64 {
+	v := c.Variance()
+	s := math.Sqrt(v)
+	return c.Mean() / (s * v) * (1 - 2*v)
+}
+
+// StdDev returns the standard deviation of the probability distribution.
+func (c Chi) StdDev() float64 {
+	return math.Sqrt(c.Variance())
+}
+
+// Survival returns the survival function (complementary CDF) at x.
+func (c Chi) Survival(x float64) float64 {
+	if x < 0 {
+		return 1
+	}
+	return mathext.GammaIncRegComp(0.5*c.K, 0.5*(x*x))
+}
+
+// Variance returns the variance of the probability distribution.
+func (c Chi) Variance() float64 {
+	m := c.Mean()
+	return math.Max(0, c.K-m*m)
+}