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0b673ab98b
* A+C: add Taesu Pyo * stat/distuv: more accurate calculation of Normal.CDF and Lognormal.CDF Fixes #577
114 lines
3.2 KiB
Go
114 lines
3.2 KiB
Go
// Copyright ©2015 The Gonum 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 distuv
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import (
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"math"
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"golang.org/x/exp/rand"
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)
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// LogNormal represents a random variable whose log is normally distributed.
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// The probability density function is given by
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// 1/(x σ √2π) exp(-(ln(x)-μ)^2)/(2σ^2))
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type LogNormal struct {
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Mu float64
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Sigma float64
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Src rand.Source
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}
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// CDF computes the value of the cumulative density function at x.
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func (l LogNormal) CDF(x float64) float64 {
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return 0.5 * math.Erfc(-(math.Log(x)-l.Mu)/(math.Sqrt2*l.Sigma))
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}
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// Entropy returns the differential entropy of the distribution.
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func (l LogNormal) Entropy() float64 {
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return 0.5 + 0.5*math.Log(2*math.Pi*l.Sigma*l.Sigma) + l.Mu
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}
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// ExKurtosis returns the excess kurtosis of the distribution.
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func (l LogNormal) ExKurtosis() float64 {
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s2 := l.Sigma * l.Sigma
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return math.Exp(4*s2) + 2*math.Exp(3*s2) + 3*math.Exp(2*s2) - 6
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}
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// LogProb computes the natural logarithm of the value of the probability density function at x.
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func (l LogNormal) LogProb(x float64) float64 {
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if x < 0 {
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return math.Inf(-1)
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}
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logx := math.Log(x)
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normdiff := (logx - l.Mu) / l.Sigma
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return -0.5*normdiff*normdiff - logx - math.Log(l.Sigma) - logRoot2Pi
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}
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// Mean returns the mean of the probability distribution.
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func (l LogNormal) Mean() float64 {
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return math.Exp(l.Mu + 0.5*l.Sigma*l.Sigma)
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}
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// Median returns the median of the probability distribution.
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func (l LogNormal) Median() float64 {
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return math.Exp(l.Mu)
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}
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// Mode returns the mode of the probability distribution.
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func (l LogNormal) Mode() float64 {
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return l.Mu
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}
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// NumParameters returns the number of parameters in the distribution.
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func (LogNormal) NumParameters() int {
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return 2
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}
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// Prob computes the value of the probability density function at x.
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func (l LogNormal) Prob(x float64) float64 {
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return math.Exp(l.LogProb(x))
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}
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// Quantile returns the inverse of the cumulative probability distribution.
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func (l LogNormal) Quantile(p float64) float64 {
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if p < 0 || p > 1 {
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panic(badPercentile)
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}
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// Formula from http://www.math.uah.edu/stat/special/LogNormal.html.
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return math.Exp(l.Mu + l.Sigma*UnitNormal.Quantile(p))
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}
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// Rand returns a random sample drawn from the distribution.
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func (l LogNormal) Rand() float64 {
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var rnd float64
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if l.Src == nil {
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rnd = rand.NormFloat64()
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} else {
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rnd = rand.New(l.Src).NormFloat64()
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}
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return math.Exp(rnd*l.Sigma + l.Mu)
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}
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// Skewness returns the skewness of the distribution.
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func (l LogNormal) Skewness() float64 {
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s2 := l.Sigma * l.Sigma
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return (math.Exp(s2) + 2) * math.Sqrt(math.Exp(s2)-1)
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}
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// StdDev returns the standard deviation of the probability distribution.
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func (l LogNormal) StdDev() float64 {
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return math.Sqrt(l.Variance())
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}
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// Survival returns the survival function (complementary CDF) at x.
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func (l LogNormal) Survival(x float64) float64 {
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return 0.5 * (1 - math.Erf((math.Log(x)-l.Mu)/(math.Sqrt2*l.Sigma)))
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}
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// Variance returns the variance of the probability distribution.
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func (l LogNormal) Variance() float64 {
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s2 := l.Sigma * l.Sigma
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return (math.Exp(s2) - 1) * math.Exp(2*l.Mu+s2)
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}
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