fixed dependencies

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

@@ -0,0 +1,145 @@
+// 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"
+
+	"gonum.org/v1/gonum/mathext"
+)
+
+// Poisson implements the Poisson distribution, a discrete probability distribution
+// that expresses the probability of a given number of events occurring in a fixed
+// interval.
+// The poisson distribution has density function:
+//
+//	f(k) = λ^k / k! e^(-λ)
+//
+// For more information, see https://en.wikipedia.org/wiki/Poisson_distribution.
+type Poisson struct {
+	// Lambda is the average number of events in an interval.
+	// Lambda must be greater than 0.
+	Lambda float64
+
+	Src rand.Source
+}
+
+// CDF computes the value of the cumulative distribution function at x.
+func (p Poisson) CDF(x float64) float64 {
+	if x < 0 {
+		return 0
+	}
+	return mathext.GammaIncRegComp(math.Floor(x+1), p.Lambda)
+}
+
+// ExKurtosis returns the excess kurtosis of the distribution.
+func (p Poisson) ExKurtosis() float64 {
+	return 1 / p.Lambda
+}
+
+// LogProb computes the natural logarithm of the value of the probability
+// density function at x.
+func (p Poisson) LogProb(x float64) float64 {
+	if x < 0 || math.Floor(x) != x {
+		return math.Inf(-1)
+	}
+	lg, _ := math.Lgamma(math.Floor(x) + 1)
+	return x*math.Log(p.Lambda) - p.Lambda - lg
+}
+
+// Mean returns the mean of the probability distribution.
+func (p Poisson) Mean() float64 {
+	return p.Lambda
+}
+
+// NumParameters returns the number of parameters in the distribution.
+func (Poisson) NumParameters() int {
+	return 1
+}
+
+// Prob computes the value of the probability density function at x.
+func (p Poisson) Prob(x float64) float64 {
+	return math.Exp(p.LogProb(x))
+}
+
+// Rand returns a random sample drawn from the distribution.
+func (p Poisson) Rand() float64 {
+	// NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5)
+	// p. 294
+	// <http://www.aip.de/groups/soe/local/numres/bookcpdf/c7-3.pdf>
+
+	rnd := rand.ExpFloat64
+	var rng *rand.Rand
+	if p.Src != nil {
+		rng = rand.New(p.Src)
+		rnd = rng.ExpFloat64
+	}
+
+	if p.Lambda < 10.0 {
+		// Use direct method.
+		var em float64
+		t := 0.0
+		for {
+			t += rnd()
+			if t >= p.Lambda {
+				break
+			}
+			em++
+		}
+		return em
+	}
+	// Generate using:
+	//  W. Hörmann. "The transformed rejection method for generating Poisson
+	//  random variables." Insurance: Mathematics and Economics
+	//  12.1 (1993): 39-45.
+
+	// Algorithm PTRS
+	rnd = rand.Float64
+	if rng != nil {
+		rnd = rng.Float64
+	}
+	b := 0.931 + 2.53*math.Sqrt(p.Lambda)
+	a := -0.059 + 0.02483*b
+	invalpha := 1.1239 + 1.1328/(b-3.4)
+	vr := 0.9277 - 3.6224/(b-2)
+	for {
+		U := rnd() - 0.5
+		V := rnd()
+		us := 0.5 - math.Abs(U)
+		k := math.Floor((2*a/us+b)*U + p.Lambda + 0.43)
+		if us >= 0.07 && V <= vr {
+			return k
+		}
+		if k <= 0 || (us < 0.013 && V > us) {
+			continue
+		}
+		lg, _ := math.Lgamma(k + 1)
+		if math.Log(V*invalpha/(a/(us*us)+b)) <= k*math.Log(p.Lambda)-p.Lambda-lg {
+			return k
+		}
+	}
+}
+
+// Skewness returns the skewness of the distribution.
+func (p Poisson) Skewness() float64 {
+	return 1 / math.Sqrt(p.Lambda)
+}
+
+// StdDev returns the standard deviation of the probability distribution.
+func (p Poisson) StdDev() float64 {
+	return math.Sqrt(p.Variance())
+}
+
+// Survival returns the survival function (complementary CDF) at x.
+func (p Poisson) Survival(x float64) float64 {
+	return 1 - p.CDF(x)
+}
+
+// Variance returns the variance of the probability distribution.
+func (p Poisson) Variance() float64 {
+	return p.Lambda
+}