PHP Class MathPHP\Probability\Distribution\Continuous\Weibull

Inheritance: extends Continuous

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Public Methods

Method	Description
CDF ( number $x, number $k, number $λ ) : float	Weibull distribution - cumulative distribution function From 0 to x (lower CDF) https://en.wikipedia.org/wiki/Weibull_distribution
PDF ( number $x, number $k, number $λ ) : float	Weibull distribution - probability density function
inverse ( number $p, $params ) : number	Inverse CDF (Quantile function)
mean ( number $k, number $λ ) : number	Mean of the distribution

f(x) = 1 - ℯ⁻⁽x/λ⁾ for x ≥ 0 f(x) = 0 for x < 0

public static CDF ( number $x, number $k, number $λ ) : float
$x	number	percentile (value to evaluate)
$k	number	shape parameter
$λ	number	scale parameter
return	float

https://en.wikipedia.org/wiki/Weibull_distribution k /x\ ᵏ⁻¹ ᵏ f(x) = - | - | ℯ⁻⁽x/λ⁾ for x ≥ 0 λ \λ/ f(x) = 0 for x < 0

public static PDF ( number $x, number $k, number $λ ) : float
$x	number	percentile (value to evaluate)
$k	number	shape parameter
$λ	number	scale parameter
return	float

Q(p;k,λ) = λ(-ln(1 - p))¹/ᵏ

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

μ = λΓ(1 + 1/k)

public static mean ( number $k, number $λ ) : number
$k	number	shape parameter
$λ	number	scale parameter
return	number