fixed dependencies

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

@@ -0,0 +1,131 @@
+// Copyright ©2017 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"
+)
+
+// Pareto implements the Pareto (Type I) distribution, a one parameter distribution
+// with support above the scale parameter.
+//
+// The density function is given by
+//
+//	(α x_m^{α})/(x^{α+1}) for x >= x_m.
+//
+// For more information, see https://en.wikipedia.org/wiki/Pareto_distribution.
+type Pareto struct {
+	// Xm is the scale parameter.
+	// Xm must be greater than 0.
+	Xm float64
+
+	// Alpha is the shape parameter.
+	// Alpha must be greater than 0.
+	Alpha float64
+
+	Src rand.Source
+}
+
+// CDF computes the value of the cumulative density function at x.
+func (p Pareto) CDF(x float64) float64 {
+	if x < p.Xm {
+		return 0
+	}
+	return -math.Expm1(p.Alpha * math.Log(p.Xm/x))
+}
+
+// Entropy returns the differential entropy of the distribution.
+func (p Pareto) Entropy() float64 {
+	return math.Log(p.Xm) - math.Log(p.Alpha) + (1 + 1/p.Alpha)
+}
+
+// ExKurtosis returns the excess kurtosis of the distribution.
+func (p Pareto) ExKurtosis() float64 {
+	if p.Alpha <= 4 {
+		return math.NaN()
+	}
+	return 6 * (p.Alpha*p.Alpha*p.Alpha + p.Alpha*p.Alpha - 6*p.Alpha - 2) / (p.Alpha * (p.Alpha - 3) * (p.Alpha - 4))
+
+}
+
+// LogProb computes the natural logarithm of the value of the probability
+// density function at x.
+func (p Pareto) LogProb(x float64) float64 {
+	if x < p.Xm {
+		return math.Inf(-1)
+	}
+	return math.Log(p.Alpha) + p.Alpha*math.Log(p.Xm) - (p.Alpha+1)*math.Log(x)
+}
+
+// Mean returns the mean of the probability distribution.
+func (p Pareto) Mean() float64 {
+	if p.Alpha <= 1 {
+		return math.Inf(1)
+	}
+	return p.Alpha * p.Xm / (p.Alpha - 1)
+}
+
+// Median returns the median of the pareto distribution.
+func (p Pareto) Median() float64 {
+	return p.Quantile(0.5)
+}
+
+// Mode returns the mode of the distribution.
+func (p Pareto) Mode() float64 {
+	return p.Xm
+}
+
+// NumParameters returns the number of parameters in the distribution.
+func (p Pareto) NumParameters() int {
+	return 2
+}
+
+// Prob computes the value of the probability density function at x.
+func (p Pareto) Prob(x float64) float64 {
+	return math.Exp(p.LogProb(x))
+}
+
+// Quantile returns the inverse of the cumulative probability distribution.
+func (p Pareto) Quantile(prob float64) float64 {
+	if prob < 0 || 1 < prob {
+		panic(badPercentile)
+	}
+	return p.Xm / math.Pow(1-prob, 1/p.Alpha)
+}
+
+// Rand returns a random sample drawn from the distribution.
+func (p Pareto) Rand() float64 {
+	var rnd float64
+	if p.Src == nil {
+		rnd = rand.ExpFloat64()
+	} else {
+		rnd = rand.New(p.Src).ExpFloat64()
+	}
+	return p.Xm * math.Exp(rnd/p.Alpha)
+}
+
+// StdDev returns the standard deviation of the probability distribution.
+func (p Pareto) StdDev() float64 {
+	return math.Sqrt(p.Variance())
+}
+
+// Survival returns the survival function (complementary CDF) at x.
+func (p Pareto) Survival(x float64) float64 {
+	if x < p.Xm {
+		return 1
+	}
+	return math.Pow(p.Xm/x, p.Alpha)
+}
+
+// Variance returns the variance of the probability distribution.
+func (p Pareto) Variance() float64 {
+	if p.Alpha <= 2 {
+		return math.Inf(1)
+	}
+	am1 := p.Alpha - 1
+	return p.Xm * p.Xm * p.Alpha / (am1 * am1 * (p.Alpha - 2))
+}