mirror of
https://github.com/gonum/gonum.git
synced 2025-10-30 02:02:09 +08:00
98 lines
2.6 KiB
Go
98 lines
2.6 KiB
Go
// 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
|
|
}
|