fixed dependencies

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

@@ -0,0 +1,124 @@
+// Copyright ©2018 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"
+)
+
+// InverseGamma implements the inverse gamma distribution, a two-parameter
+// continuous distribution with support over the positive real numbers. The
+// inverse gamma distribution is the same as the distribution of the reciprocal
+// of a gamma distributed random variable.
+//
+// The inverse gamma distribution has density function
+//
+//	β^α / Γ(α) x^(-α-1)e^(-β/x)
+//
+// For more information, see https://en.wikipedia.org/wiki/Inverse-gamma_distribution
+type InverseGamma struct {
+	// Alpha is the shape parameter of the distribution. Alpha must be greater than 0.
+	Alpha float64
+	// Beta is the scale 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 (g InverseGamma) CDF(x float64) float64 {
+	if x < 0 {
+		return 0
+	}
+	// TODO(btracey): Replace this with a direct call to the upper regularized
+	// gamma function if mathext gets it.
+	//return 1 - mathext.GammaInc(g.Alpha, g.Beta/x)
+	return mathext.GammaIncRegComp(g.Alpha, g.Beta/x)
+}
+
+// ExKurtosis returns the excess kurtosis of the distribution.
+func (g InverseGamma) ExKurtosis() float64 {
+	if g.Alpha <= 4 {
+		return math.Inf(1)
+	}
+	return (30*g.Alpha - 66) / (g.Alpha - 3) / (g.Alpha - 4)
+}
+
+// LogProb computes the natural logarithm of the value of the probability
+// density function at x.
+func (g InverseGamma) LogProb(x float64) float64 {
+	if x <= 0 {
+		return math.Inf(-1)
+	}
+	a := g.Alpha
+	b := g.Beta
+	lg, _ := math.Lgamma(a)
+	return a*math.Log(b) - lg + (-a-1)*math.Log(x) - b/x
+}
+
+// Mean returns the mean of the probability distribution.
+func (g InverseGamma) Mean() float64 {
+	if g.Alpha <= 1 {
+		return math.Inf(1)
+	}
+	return g.Beta / (g.Alpha - 1)
+}
+
+// Mode returns the mode of the distribution.
+func (g InverseGamma) Mode() float64 {
+	return g.Beta / (g.Alpha + 1)
+}
+
+// NumParameters returns the number of parameters in the distribution.
+func (InverseGamma) NumParameters() int {
+	return 2
+}
+
+// Prob computes the value of the probability density function at x.
+func (g InverseGamma) Prob(x float64) float64 {
+	return math.Exp(g.LogProb(x))
+}
+
+// Quantile returns the inverse of the cumulative distribution function.
+func (g InverseGamma) Quantile(p float64) float64 {
+	if p < 0 || 1 < p {
+		panic(badPercentile)
+	}
+	return (1 / (mathext.GammaIncRegCompInv(g.Alpha, p))) * g.Beta
+}
+
+// Rand returns a random sample drawn from the distribution.
+//
+// Rand panics if either alpha or beta is <= 0.
+func (g InverseGamma) Rand() float64 {
+	// TODO(btracey): See if there is a more direct way to sample.
+	return 1 / Gamma(g).Rand()
+}
+
+// Survival returns the survival function (complementary CDF) at x.
+func (g InverseGamma) Survival(x float64) float64 {
+	if x < 0 {
+		return 1
+	}
+	return mathext.GammaIncReg(g.Alpha, g.Beta/x)
+}
+
+// StdDev returns the standard deviation of the probability distribution.
+func (g InverseGamma) StdDev() float64 {
+	return math.Sqrt(g.Variance())
+}
+
+// Variance returns the variance of the probability distribution.
+func (g InverseGamma) Variance() float64 {
+	if g.Alpha <= 2 {
+		return math.Inf(1)
+	}
+	v := g.Beta / (g.Alpha - 1)
+	return v * v / (g.Alpha - 2)
+}