Probabilities::GenExtValueCDF Function

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

Generalized extreme value (GEV) cumulative distribution function (CDF).

#	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 CDF 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:

With z=(x-mu)/sigma the Generalized Extreme Value CDF is

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

The equivalent scipy.stats genextreme shape is $c=-k$ . It is monotone non-decreasing. 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