PHP Class MathPHP\Probability\Distribution\Continuous\LogLogistic

https://en.wikipedia.org/wiki/Log-logistic_distribution

Inheritance: extends Continuous

Show file Open project: markrogoyski/math-php

Public Methods

Method	Description
CDF ( number $x, number $α, number $β )	Cumulative distribution function
PDF ( number $x, number $α, number $β ) : number	Probability density function
inverse ( number $p, $params ) : number	Inverse CDF (Quantile function)
mean ( number $α, number $β ) : number	Mean of the distribution

1 F(x; α, β) = ----------- 1 + (x/α)⁻ᵝ

public static CDF ( number $x, number $α, number $β )
$x	number	(x > 0)
$α	number	scale parameter (α > 0)
$β	number	shape parameter (β > 0)

(β/α)(x/α)ᵝ⁻¹ f(x; α, β) = ------------- (1 + (x/α)ᵝ)²

public static PDF ( number $x, number $α, number $β ) : number
$x	number	(x > 0)
$α	number	scale parameter (α > 0)
$β	number	shape parameter (β > 0)
return	number

p \ 1/β F⁻¹(p;α,β) = α | ----- | \ 1 - p /

public static inverse ( number $p, $params ) : number
$p	number
return	number

απ / β μ = -------- if β > 1, else undefined sin(π/β)

public static mean ( number $α, number $β ) : number
$α	number	scale parameter (α > 0)
$β	number	shape parameter (β > 0)
return	number