142 lines
3.3 KiB
Go
142 lines
3.3 KiB
Go
// Copyright 2015 The Go Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package stats
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import (
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"math"
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"math/rand"
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)
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// NormalDist is a normal (Gaussian) distribution with mean Mu and
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// standard deviation Sigma.
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type NormalDist struct {
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Mu, Sigma float64
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}
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// StdNormal is the standard normal distribution (Mu = 0, Sigma = 1)
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var StdNormal = NormalDist{0, 1}
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// 1/sqrt(2 * pi)
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const invSqrt2Pi = 0.39894228040143267793994605993438186847585863116493465766592583
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func (n NormalDist) PDF(x float64) float64 {
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z := x - n.Mu
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return math.Exp(-z*z/(2*n.Sigma*n.Sigma)) * invSqrt2Pi / n.Sigma
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}
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func (n NormalDist) pdfEach(xs []float64) []float64 {
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res := make([]float64, len(xs))
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if n.Mu == 0 && n.Sigma == 1 {
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// Standard normal fast path
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for i, x := range xs {
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res[i] = math.Exp(-x*x/2) * invSqrt2Pi
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}
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} else {
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a := -1 / (2 * n.Sigma * n.Sigma)
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b := invSqrt2Pi / n.Sigma
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for i, x := range xs {
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z := x - n.Mu
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res[i] = math.Exp(z*z*a) * b
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}
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}
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return res
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}
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func (n NormalDist) CDF(x float64) float64 {
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return math.Erfc(-(x-n.Mu)/(n.Sigma*math.Sqrt2)) / 2
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}
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func (n NormalDist) cdfEach(xs []float64) []float64 {
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res := make([]float64, len(xs))
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a := 1 / (n.Sigma * math.Sqrt2)
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for i, x := range xs {
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res[i] = math.Erfc(-(x-n.Mu)*a) / 2
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}
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return res
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}
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func (n NormalDist) InvCDF(p float64) (x float64) {
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// This is based on Peter John Acklam's inverse normal CDF
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// algorithm: http://home.online.no/~pjacklam/notes/invnorm/
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const (
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a1 = -3.969683028665376e+01
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a2 = 2.209460984245205e+02
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a3 = -2.759285104469687e+02
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a4 = 1.383577518672690e+02
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a5 = -3.066479806614716e+01
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a6 = 2.506628277459239e+00
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b1 = -5.447609879822406e+01
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b2 = 1.615858368580409e+02
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b3 = -1.556989798598866e+02
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b4 = 6.680131188771972e+01
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b5 = -1.328068155288572e+01
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c1 = -7.784894002430293e-03
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c2 = -3.223964580411365e-01
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c3 = -2.400758277161838e+00
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c4 = -2.549732539343734e+00
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c5 = 4.374664141464968e+00
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c6 = 2.938163982698783e+00
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d1 = 7.784695709041462e-03
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d2 = 3.224671290700398e-01
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d3 = 2.445134137142996e+00
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d4 = 3.754408661907416e+00
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plow = 0.02425
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phigh = 1 - plow
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)
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if p < 0 || p > 1 {
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return nan
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} else if p == 0 {
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return -inf
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} else if p == 1 {
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return inf
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}
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if p < plow {
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// Rational approximation for lower region.
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q := math.Sqrt(-2 * math.Log(p))
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x = (((((c1*q+c2)*q+c3)*q+c4)*q+c5)*q + c6) /
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((((d1*q+d2)*q+d3)*q+d4)*q + 1)
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} else if phigh < p {
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// Rational approximation for upper region.
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q := math.Sqrt(-2 * math.Log(1-p))
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x = -(((((c1*q+c2)*q+c3)*q+c4)*q+c5)*q + c6) /
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((((d1*q+d2)*q+d3)*q+d4)*q + 1)
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} else {
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// Rational approximation for central region.
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q := p - 0.5
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r := q * q
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x = (((((a1*r+a2)*r+a3)*r+a4)*r+a5)*r + a6) * q /
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(((((b1*r+b2)*r+b3)*r+b4)*r+b5)*r + 1)
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}
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// Refine approximation.
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e := 0.5*math.Erfc(-x/math.Sqrt2) - p
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u := e * math.Sqrt(2*math.Pi) * math.Exp(x*x/2)
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x = x - u/(1+x*u/2)
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// Adjust from standard normal.
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return x*n.Sigma + n.Mu
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}
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func (n NormalDist) Rand(r *rand.Rand) float64 {
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var x float64
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if r == nil {
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x = rand.NormFloat64()
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} else {
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x = r.NormFloat64()
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}
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return x*n.Sigma + n.Mu
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}
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func (n NormalDist) Bounds() (float64, float64) {
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const stddevs = 3
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return n.Mu - stddevs*n.Sigma, n.Mu + stddevs*n.Sigma
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}
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