Probabilities::GenParetoCDFInv Function

double GenParetoCDFInv(double p, double k, double Mu, double sigma);

Generalized Pareto (GPD) percent point function (PPF, quantile / inverse CDF).

#	Name	Type	Description
1	p	double	Probability, real value on the closed interval [0,1].
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 value x such that GenParetoCDF(x,k,Mu,sigma)=p, using shape k, location Mu and positive scale sigma. Returns NaN if sigma<=0 or p is outside [0,1].

Remarks:

The GPD inverse CDF has a closed form. With z defined below,

CDFInv(p | k,mu,sigma) = mu + sigma z ,   z = { ((1-p)^(-k)-1)/k,  if k != 0
                                              { [1.2ex] -ln(1-p),  if k=0   ,   0 < p < 1 .

Boundary values: z=0 at p=0; at p=1, $z=-1/k`for`k<0`and`z=+\infty`for`k\ge 0$ . Returns NaN for sigma<=0 or p outside [0,1].

See Also: Probabilities::GenParetoPDF, Probabilities::GenParetoCDF

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