Probabilities::GenExtValuePDF Function

double GenExtValuePDF(double x, double k, double Mu, double sigma);

Generalized extreme value (GEV) probability density function (PDF).

#	Name	Type	Description
1	x	double	Distribution domain, real value; valid when k*(x-Mu)/sigma > -1.
2	k	double	Distribution shape parameter, real value.
3	Mu	double	Distribution location parameter, real value.
4	sigma	double	Distribution scale parameter, positive real value (sigma>0).

Returns: the Generalized extreme value PDF for value x using shape k, location Mu and positive scale sigma. Returns NaN if sigma<=0, or (for k<>0) if 1+k(x-Mu)/sigma<=0.

Remarks:

Calculates the Generalized extreme value density. With z=(x-mu)/sigma,

PDF(x | k,mu,sigma) = { 1/sigma(1+k z)^(-1/k-1) exp[-(1+k z)^(-1/k)],  if 1+k z > 0
                      { [1.2ex] 1/sigmaexp[-exp[-z]-z],  if k=0   ,   z=(x-mu)/sigma .

This shape convention uses (1+k z)^(-1/k); the equivalent scipy.stats genextreme shape is $c=-k$ . Returns NaN for sigma<=0, or when 1+k z <= 0 for k != 0.

Declared in Dew::Math::Units::Probabilities · Dew.Math/Units.Probabilities.h · Cross-compiler