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133 lines
2.9 KiB
Go
133 lines
2.9 KiB
Go
// Copyright ©2016 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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// Bernoulli represents a random variable whose value is 1 with probability p and
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// value of zero with probability 1-P. The value of P must be between 0 and 1.
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// More information at https://en.wikipedia.org/wiki/Bernoulli_distribution.
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type Bernoulli struct {
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P 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 (b Bernoulli) CDF(x float64) float64 {
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if x < 0 {
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return 0
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}
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if x < 1 {
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return 1 - b.P
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}
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return 1
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}
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// Entropy returns the entropy of the distribution.
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func (b Bernoulli) Entropy() float64 {
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if b.P == 0 {
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return 0
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}
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if b.P == 1 {
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return 1
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}
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q := 1 - b.P
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return -b.P*math.Log(b.P) - q*math.Log(q)
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}
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// ExKurtosis returns the excess kurtosis of the distribution.
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func (b Bernoulli) ExKurtosis() float64 {
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pq := b.P * (1 - b.P)
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return (1 - 6*pq) / pq
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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 (b Bernoulli) LogProb(x float64) float64 {
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if x == 0 {
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return math.Log(1 - b.P)
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}
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if x == 1 {
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return math.Log(b.P)
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}
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return math.Inf(-1)
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}
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// Mean returns the mean of the probability distribution.
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func (b Bernoulli) Mean() float64 {
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return b.P
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}
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// Median returns the median of the probability distribution.
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func (b Bernoulli) Median() float64 {
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p := b.P
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switch {
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case p < 0.5:
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return 0
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case p > 0.5:
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return 1
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default:
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return 0.5
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}
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}
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// NumParameters returns the number of parameters in the distribution.
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func (Bernoulli) NumParameters() int {
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return 1
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}
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// Prob computes the value of the probability distribution at x.
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func (b Bernoulli) Prob(x float64) float64 {
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return math.Exp(b.LogProb(x))
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}
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// Quantile returns the inverse of the cumulative probability distribution.
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func (b Bernoulli) Quantile(p float64) float64 {
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if p < 0 || 1 < p {
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panic(badPercentile)
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}
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if p < 1-b.P {
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return 0
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}
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return 1
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}
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// Rand returns a random sample drawn from the distribution.
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func (b Bernoulli) Rand() float64 {
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var rnd float64
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if b.Src == nil {
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rnd = rand.Float64()
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} else {
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rnd = rand.New(b.Src).Float64()
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}
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if rnd < b.P {
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return 1
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}
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return 0
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}
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// Skewness returns the skewness of the distribution.
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func (b Bernoulli) Skewness() float64 {
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return (1 - 2*b.P) / math.Sqrt(b.P*(1-b.P))
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}
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// StdDev returns the standard deviation of the probability distribution.
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func (b Bernoulli) StdDev() float64 {
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return math.Sqrt(b.Variance())
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}
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// Survival returns the survival function (complementary CDF) at x.
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func (b Bernoulli) Survival(x float64) float64 {
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return 1 - b.CDF(x)
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}
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// Variance returns the variance of the probability distribution.
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func (b Bernoulli) Variance() float64 {
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return b.P * (1 - b.P)
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}
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