Probabilities::GenParetoPDF Function

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

Generalized Pareto (GPD) probability density function (PDF).

#NameTypeDescription
1xdoubleDistribution domain, real value; if k >= 0 valid on (Mu, +Inf), if k < 0 valid when 0 <= (x-Mu)/sigma <= -1/k.
2kdoubleDistribution shape parameter, real value.
3MudoubleDistribution location parameter, real value.
4sigmadoubleDistribution scale parameter, positive real value (sigma>0).

Returns: the Generalized Pareto 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 Pareto density. With z=(x-mu)/sigma,

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

This shape convention matches scipy.stats genpareto with c=k. Returns NaN for sigma<=0, or when 1+k z <= 0 for k < 0.

See Also: Probabilities::GenParetoCDF, Probabilities::GenParetoCDFInv
Declared in Dew::Math::Units::Probabilities · Dew.Math/Units.Probabilities.h · Cross-compiler