fixed dependencies

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

@@ -0,0 +1,152 @@
+// 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"
+)
+
+// Beta implements the Beta distribution, a two-parameter continuous distribution
+// with support between 0 and 1.
+//
+// The beta distribution has density function
+//
+//	x^(α-1) * (1-x)^(β-1) * Γ(α+β) / (Γ(α)*Γ(β))
+//
+// For more information, see https://en.wikipedia.org/wiki/Beta_distribution
+type Beta struct {
+	// Alpha is the left shape parameter of the distribution. Alpha must be greater
+	// than 0.
+	Alpha float64
+	// Beta is the right shape parameter of the distribution. Beta must be greater
+	// than 0.
+	Beta float64
+
+	Src rand.Source
+}
+
+// CDF computes the value of the cumulative distribution function at x.
+func (b Beta) CDF(x float64) float64 {
+	if x <= 0 {
+		return 0
+	}
+	if x >= 1 {
+		return 1
+	}
+	return mathext.RegIncBeta(b.Alpha, b.Beta, x)
+}
+
+// Entropy returns the differential entropy of the distribution.
+func (b Beta) Entropy() float64 {
+	if b.Alpha <= 0 || b.Beta <= 0 {
+		panic("beta: negative parameters")
+	}
+	return mathext.Lbeta(b.Alpha, b.Beta) - (b.Alpha-1)*mathext.Digamma(b.Alpha) -
+		(b.Beta-1)*mathext.Digamma(b.Beta) + (b.Alpha+b.Beta-2)*mathext.Digamma(b.Alpha+b.Beta)
+}
+
+// ExKurtosis returns the excess kurtosis of the distribution.
+func (b Beta) ExKurtosis() float64 {
+	num := 6 * ((b.Alpha-b.Beta)*(b.Alpha-b.Beta)*(b.Alpha+b.Beta+1) - b.Alpha*b.Beta*(b.Alpha+b.Beta+2))
+	den := b.Alpha * b.Beta * (b.Alpha + b.Beta + 2) * (b.Alpha + b.Beta + 3)
+	return num / den
+}
+
+// LogProb computes the natural logarithm of the value of the probability
+// density function at x.
+func (b Beta) LogProb(x float64) float64 {
+	if x < 0 || x > 1 {
+		return math.Inf(-1)
+	}
+
+	if b.Alpha <= 0 || b.Beta <= 0 {
+		panic("beta: negative parameters")
+	}
+
+	lab, _ := math.Lgamma(b.Alpha + b.Beta)
+	la, _ := math.Lgamma(b.Alpha)
+	lb, _ := math.Lgamma(b.Beta)
+	var lx float64
+	if b.Alpha != 1 {
+		lx = (b.Alpha - 1) * math.Log(x)
+	}
+	var l1mx float64
+	if b.Beta != 1 {
+		l1mx = (b.Beta - 1) * math.Log(1-x)
+	}
+	return lab - la - lb + lx + l1mx
+}
+
+// Mean returns the mean of the probability distribution.
+func (b Beta) Mean() float64 {
+	return b.Alpha / (b.Alpha + b.Beta)
+}
+
+// Mode returns the mode of the distribution.
+//
+// Mode returns NaN if both parameters are less than or equal to 1 as a special case,
+// 0 if only Alpha <= 1 and 1 if only Beta <= 1.
+func (b Beta) Mode() float64 {
+	if b.Alpha <= 1 {
+		if b.Beta <= 1 {
+			return math.NaN()
+		}
+		return 0
+	}
+	if b.Beta <= 1 {
+		return 1
+	}
+	return (b.Alpha - 1) / (b.Alpha + b.Beta - 2)
+}
+
+// NumParameters returns the number of parameters in the distribution.
+func (b Beta) NumParameters() int {
+	return 2
+}
+
+// Prob computes the value of the probability density function at x.
+func (b Beta) Prob(x float64) float64 {
+	return math.Exp(b.LogProb(x))
+}
+
+// Quantile returns the inverse of the cumulative distribution function.
+func (b Beta) Quantile(p float64) float64 {
+	if p < 0 || p > 1 {
+		panic(badPercentile)
+	}
+	return mathext.InvRegIncBeta(b.Alpha, b.Beta, p)
+}
+
+// Rand returns a random sample drawn from the distribution.
+func (b Beta) Rand() float64 {
+	ga := Gamma{Alpha: b.Alpha, Beta: 1, Src: b.Src}.Rand()
+	gb := Gamma{Alpha: b.Beta, Beta: 1, Src: b.Src}.Rand()
+	return ga / (ga + gb)
+}
+
+// StdDev returns the standard deviation of the probability distribution.
+func (b Beta) StdDev() float64 {
+	return math.Sqrt(b.Variance())
+}
+
+// Survival returns the survival function (complementary CDF) at x.
+func (b Beta) Survival(x float64) float64 {
+	switch {
+	case x <= 0:
+		return 1
+	case x >= 1:
+		return 0
+	}
+	return mathext.RegIncBeta(b.Beta, b.Alpha, 1-x)
+}
+
+// Variance returns the variance of the probability distribution.
+func (b Beta) Variance() float64 {
+	return b.Alpha * b.Beta / ((b.Alpha + b.Beta) * (b.Alpha + b.Beta) * (b.Alpha + b.Beta + 1))
+}