fixed dependencies

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

@@ -0,0 +1,113 @@
+// Copyright ©2020 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"
+)
+
+// AlphaStable represents an α-stable distribution with four parameters.
+// See https://en.wikipedia.org/wiki/Stable_distribution for more information.
+type AlphaStable struct {
+	// Alpha is the stability parameter.
+	// It is valid within the range 0 < α ≤ 2.
+	Alpha float64
+	// Beta is the skewness parameter.
+	// It is valid within the range -1 ≤ β ≤ 1.
+	Beta float64
+	// C is the scale parameter.
+	// It is valid when positive.
+	C float64
+	// Mu is the location parameter.
+	Mu  float64
+	Src rand.Source
+}
+
+// ExKurtosis returns the excess kurtosis of the distribution.
+// ExKurtosis returns NaN when Alpha != 2.
+func (a AlphaStable) ExKurtosis() float64 {
+	if a.Alpha == 2 {
+		return 0
+	}
+	return math.NaN()
+}
+
+// Mean returns the mean of the probability distribution.
+// Mean returns NaN when Alpha <= 1.
+func (a AlphaStable) Mean() float64 {
+	if a.Alpha > 1 {
+		return a.Mu
+	}
+	return math.NaN()
+}
+
+// Median returns the median of the distribution.
+// Median panics when Beta != 0, because then the mode is not analytically
+// expressible.
+func (a AlphaStable) Median() float64 {
+	if a.Beta == 0 {
+		return a.Mu
+	}
+	panic("distuv: cannot compute Median for Beta != 0")
+}
+
+// Mode returns the mode of the distribution.
+// Mode panics when Beta != 0, because then the mode is not analytically
+// expressible.
+func (a AlphaStable) Mode() float64 {
+	if a.Beta == 0 {
+		return a.Mu
+	}
+	panic("distuv: cannot compute Mode for Beta != 0")
+}
+
+// NumParameters returns the number of parameters in the distribution.
+func (a AlphaStable) NumParameters() int {
+	return 4
+}
+
+// Rand returns a random sample drawn from the distribution.
+func (a AlphaStable) Rand() float64 {
+	// From https://en.wikipedia.org/wiki/Stable_distribution#Simulation_of_stable_variables
+	const halfPi = math.Pi / 2
+	u := Uniform{-halfPi, halfPi, a.Src}.Rand()
+	w := Exponential{1, a.Src}.Rand()
+	if a.Alpha == 1 {
+		f := halfPi + a.Beta*u
+		x := (f*math.Tan(u) - a.Beta*math.Log(halfPi*w*math.Cos(u)/f)) / halfPi
+		return a.C*(x+a.Beta*math.Log(a.C)/halfPi) + a.Mu
+	}
+	zeta := -a.Beta * math.Tan(halfPi*a.Alpha)
+	xi := math.Atan(-zeta) / a.Alpha
+	f := a.Alpha * (u + xi)
+	g := math.Sqrt(1+zeta*zeta) * math.Pow(math.Cos(u-f)/w, 1-a.Alpha) / math.Cos(u)
+	x := math.Pow(g, 1/a.Alpha) * math.Sin(f)
+	return a.C*x + a.Mu
+}
+
+// Skewness returns the skewness of the distribution.
+// Skewness returns NaN when Alpha != 2.
+func (a AlphaStable) Skewness() float64 {
+	if a.Alpha == 2 {
+		return 0
+	}
+	return math.NaN()
+}
+
+// StdDev returns the standard deviation of the probability distribution.
+func (a AlphaStable) StdDev() float64 {
+	return math.Sqrt(a.Variance())
+}
+
+// Variance returns the variance of the probability distribution.
+// Variance returns +Inf when Alpha != 2.
+func (a AlphaStable) Variance() float64 {
+	if a.Alpha == 2 {
+		return 2 * a.C * a.C
+	}
+	return math.Inf(1)
+}