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// Copyright ©2021 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"
)
// Logistic implements the Logistic distribution, a two-parameter distribution with support on the real axis.
// Its cumulative distribution function is the logistic function.
//
// General form of probability density function for Logistic distribution is
//
// E(x) / (s * (1 + E(x))^2)
// where E(x) = exp(-(x-μ)/s)
//
// For more information, see https://en.wikipedia.org/wiki/Logistic_distribution.
type Logistic struct {
Mu float64 // Mean value
S float64 // Scale parameter proportional to standard deviation
}
// CDF computes the value of the cumulative density function at x.
func (l Logistic) CDF(x float64) float64 {
return 1 / (1 + math.Exp(-(x-l.Mu)/l.S))
}
// ExKurtosis returns the excess kurtosis of the distribution.
func (l Logistic) ExKurtosis() float64 {
return 6.0 / 5.0
}
// LogProb computes the natural logarithm of the value of the probability
// density function at x.
func (l Logistic) LogProb(x float64) float64 {
return x - 2*math.Log(math.Exp(x)+1)
}
// Mean returns the mean of the probability distribution.
func (l Logistic) Mean() float64 {
return l.Mu
}
// Mode returns the mode of the distribution.
//
// It is same as Mean for Logistic distribution.
func (l Logistic) Mode() float64 {
return l.Mu
}
// Median returns the median of the distribution.
//
// It is same as Mean for Logistic distribution.
func (l Logistic) Median() float64 {
return l.Mu
}
// NumParameters returns the number of parameters in the distribution.
//
// Always returns 2.
func (l Logistic) NumParameters() int {
return 2
}
// Prob computes the value of the probability density function at x.
func (l Logistic) Prob(x float64) float64 {
E := math.Exp(-(x - l.Mu) / l.S)
return E / (l.S * math.Pow(1+E, 2))
}
// Quantile returns the inverse of the cumulative distribution function.
func (l Logistic) Quantile(p float64) float64 {
return l.Mu + l.S*math.Log(p/(1-p))
}
// Skewness returns the skewness of the distribution.
//
// Always 0 for Logistic distribution.
func (l Logistic) Skewness() float64 {
return 0
}
// StdDev returns the standard deviation of the probability distribution.
func (l Logistic) StdDev() float64 {
return l.S * math.Pi / sqrt3
}
// Survival returns the survival function (complementary CDF) at x.
func (l Logistic) Survival(x float64) float64 {
return 1 - l.CDF(x)
}
// Variance returns the variance of the probability distribution.
func (l Logistic) Variance() float64 {
return l.S * l.S * math.Pi * math.Pi / 3
}
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