PHP Class MathPHP\Probability\Distribution\Continuous\Cauchy

Inheritance: extends Continuous

Show file Open project: markrogoyski/math-php

Public Methods

Method	Description
CDF ( number $x, number $x₀, integer $γ ) : number	Cumulative distribution function Calculate the cumulative value value up to a point, left tail.
PDF ( number $x, number $x₀, integer $γ ) : number	Probability density function
inverse ( number $p, $params ) : number	Inverse CDF (Quantile function)
mean ( number $x₀, integer $γ ) : null	Mean of the distribution (undefined)
median ( number $x₀, integer $γ ) : x₀	Meadian of the distribution
mode ( number $x₀, integer $γ ) : x₀	Mode of the distribution

Cumulative distribution function Calculate the cumulative value value up to a point, left tail.

public static CDF ( number $x, number $x₀, integer $γ ) : number
$x	number
$x₀	number	location
$γ	integer	scale
return	number

1 -------------------------- ┌ / x - x₀ \ ² ┐ πγ | 1 + | ---------| | └ \ γ / ┘

public static PDF ( number $x, number $x₀, integer $γ ) : number
$x	number
$x₀	number	location
$γ	integer	scale
return	number

Q(p;x₀,γ) = x₀ + γ tan[π(p - ½)]

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

μ is undefined

public static mean ( number $x₀, integer $γ ) : null
$x₀	number	location
$γ	integer	scale
return	null

Meadian of the distribution

public static median ( number $x₀, integer $γ ) : x₀
$x₀	number	location
$γ	integer	scale
return	x₀

Mode of the distribution

public static mode ( number $x₀, integer $γ ) : x₀
$x₀	number	location
$γ	integer	scale
return	x₀