Probabilities::GumbelCDF Function

Overload List

#	Signature	Description
1	double GumbelCDF(double x, double Mu, double beta, bool minimum);	Gumbel cumulative distribution function (CDF).
2	void GumbelCDF(TDenseMtxVec X, double* Mu, double beta, bool minimum, TDenseMtxVec *Res);	Gumbel distribution CDF (vectorized).

Gumbel cumulative distribution function (CDF).

#	Name	Type	Description
1	x	double	Function domain, real value.
2	Mu	double	Location parameter, real value.
3	beta	double	Scale parameter, positive real value.
4	minimum	bool	Selects the distribution sign. If true, the minimum (left) Gumbel CDF is computed; if false, the maximum (right) Gumbel CDF.

Returns: the Gumbel cumulative distribution function (CDF) for value x using the parameters Mu and beta. For beta <= 0 the result is NAN.

Remarks:

With z = (x - Mu) / beta, the Gumbel cumulative distribution function is

CDF(x| mu,beta)={ 1-e^(-e^z),  if amp; minimum
                { [4pt] e^(-e^(-z)),  if amp; maximum

Domain: x any real value, Mu any real value, scale beta > 0; the result rises monotonically from 0 to 1. For beta <= 0 the result is NAN.

See Also: Probabilities::GumbelPDF, Probabilities::GumbelCDFInv

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

Gumbel distribution CDF (vectorized).

#	Name	Type	Description
1	X	TDenseMtxVec *	Defines distribution domain, real vector or matrix.
2	Mu	double	Defines the location parameter.
3	beta	double	Defines the scale parameter, positive real value.
4	minimum	bool	Defines maximum or minimum Gumbel distrubution. If true, the routine calculates minimum Gumbel PDF.
5	Res	TDenseMtxVec *	After calculation stores the CDF calculated from X, Mu, and beta. Length and Complex properties of Res are adjusted automatically to match Length and Complex properties of X.

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