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