fixed dependencies

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

@@ -0,0 +1,162 @@
+// 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"
+)
+
+const logPi = 1.1447298858494001741 // http://oeis.org/A053510
+
+// StudentsT implements the three-parameter Student's T distribution, a distribution
+// over the real numbers.
+//
+// The Student's T distribution has density function
+//
+//	Γ((ν+1)/2) / (sqrt(νπ) Γ(ν/2) σ) (1 + 1/ν * ((x-μ)/σ)^2)^(-(ν+1)/2)
+//
+// The Student's T distribution approaches the normal distribution as ν → ∞.
+//
+// For more information, see https://en.wikipedia.org/wiki/Student%27s_t-distribution,
+// specifically https://en.wikipedia.org/wiki/Student%27s_t-distribution#Non-standardized_Student.27s_t-distribution .
+//
+// The standard Student's T distribution is with Mu = 0, and Sigma = 1.
+type StudentsT struct {
+	// Mu is the location parameter of the distribution, and the mean of the
+	// distribution
+	Mu float64
+
+	// Sigma is the scale parameter of the distribution. It is related to the
+	// standard deviation by std = Sigma * sqrt(Nu/(Nu-2))
+	Sigma float64
+
+	// Nu is the shape parameter of the distribution, representing the number of
+	// degrees of the distribution, and one less than the number of observations
+	// from a Normal distribution.
+	Nu float64
+
+	Src rand.Source
+}
+
+// CDF computes the value of the cumulative distribution function at x.
+func (s StudentsT) CDF(x float64) float64 {
+	// transform to standard normal
+	y := (x - s.Mu) / s.Sigma
+	if y == 0 {
+		return 0.5
+	}
+	// For t > 0
+	// F(y) = 1 - 0.5 * I_t(y)(nu/2, 1/2)
+	// t(y) = nu/(y^2 + nu)
+	// and 1 - F(y) for t < 0
+	t := s.Nu / (y*y + s.Nu)
+	if y > 0 {
+		return 1 - 0.5*mathext.RegIncBeta(0.5*s.Nu, 0.5, t)
+	}
+	return 0.5 * mathext.RegIncBeta(s.Nu/2, 0.5, t)
+}
+
+// LogProb computes the natural logarithm of the value of the probability
+// density function at x.
+func (s StudentsT) LogProb(x float64) float64 {
+	g1, _ := math.Lgamma((s.Nu + 1) / 2)
+	g2, _ := math.Lgamma(s.Nu / 2)
+	z := (x - s.Mu) / s.Sigma
+	return g1 - g2 - 0.5*math.Log(s.Nu) - 0.5*logPi - math.Log(s.Sigma) - ((s.Nu+1)/2)*math.Log(1+z*z/s.Nu)
+}
+
+// Mean returns the mean of the probability distribution.
+func (s StudentsT) Mean() float64 {
+	return s.Mu
+}
+
+// Mode returns the mode of the distribution.
+func (s StudentsT) Mode() float64 {
+	return s.Mu
+}
+
+// NumParameters returns the number of parameters in the distribution.
+func (StudentsT) NumParameters() int {
+	return 3
+}
+
+// Prob computes the value of the probability density function at x.
+func (s StudentsT) Prob(x float64) float64 {
+	return math.Exp(s.LogProb(x))
+}
+
+// Quantile returns the inverse of the cumulative distribution function.
+func (s StudentsT) Quantile(p float64) float64 {
+	if p < 0 || p > 1 {
+		panic(badPercentile)
+	}
+	// F(x) = 1 - 0.5 * I_t(x)(nu/2, 1/2)
+	// t(x) = nu/(t^2 + nu)
+	if p == 0.5 {
+		return s.Mu
+	}
+	var y float64
+	if p > 0.5 {
+		// Know t > 0
+		t := mathext.InvRegIncBeta(s.Nu/2, 0.5, 2*(1-p))
+		y = math.Sqrt(s.Nu * (1 - t) / t)
+	} else {
+		t := mathext.InvRegIncBeta(s.Nu/2, 0.5, 2*p)
+		y = -math.Sqrt(s.Nu * (1 - t) / t)
+	}
+	// Convert out of standard normal
+	return y*s.Sigma + s.Mu
+}
+
+// Rand returns a random sample drawn from the distribution.
+func (s StudentsT) Rand() float64 {
+	// http://www.math.uah.edu/stat/special/Student.html
+	n := Normal{0, 1, s.Src}.Rand()
+	c := Gamma{s.Nu / 2, 0.5, s.Src}.Rand()
+	z := n / math.Sqrt(c/s.Nu)
+	return z*s.Sigma + s.Mu
+}
+
+// StdDev returns the standard deviation of the probability distribution.
+//
+// The standard deviation is undefined for ν <= 1, and this returns math.NaN().
+func (s StudentsT) StdDev() float64 {
+	return math.Sqrt(s.Variance())
+}
+
+// Survival returns the survival function (complementary CDF) at x.
+func (s StudentsT) Survival(x float64) float64 {
+	// transform to standard normal
+	y := (x - s.Mu) / s.Sigma
+	if y == 0 {
+		return 0.5
+	}
+	// For t > 0
+	// F(y) = 1 - 0.5 * I_t(y)(nu/2, 1/2)
+	// t(y) = nu/(y^2 + nu)
+	// and 1 - F(y) for t < 0
+	t := s.Nu / (y*y + s.Nu)
+	if y > 0 {
+		return 0.5 * mathext.RegIncBeta(s.Nu/2, 0.5, t)
+	}
+	return 1 - 0.5*mathext.RegIncBeta(s.Nu/2, 0.5, t)
+}
+
+// Variance returns the variance of the probability distribution.
+//
+// The variance is undefined for ν <= 1, and this returns math.NaN().
+func (s StudentsT) Variance() float64 {
+	if s.Nu <= 1 {
+		return math.NaN()
+	}
+	if s.Nu <= 2 {
+		return math.Inf(1)
+	}
+	return s.Sigma * s.Sigma * s.Nu / (s.Nu - 2)
+}