Probabilities::GumbelPDF Function

Overload List

#SignatureDescription
1double GumbelPDF(double x, double Mu, double beta, bool minimum);Gumbel probability density function (PDF).
2void GumbelPDF(TDenseMtxVec *X, double Mu, double beta, bool minimum, TDenseMtxVec *Res);Gumbel distribution PDF (vectorized).

Overload 1: double GumbelPDF(double x, double Mu, double beta, bool minimum);

Gumbel probability density function (PDF).

#NameTypeDescription
1xdoubleFunction domain, real value.
2MudoubleLocation parameter, real value.
3betadoubleScale parameter, positive real value.
4minimumboolSelects the distribution sign. If true, the minimum (left/smallest) Gumbel PDF is computed; if false, the maximum (right/largest) Gumbel PDF.

Returns: the Gumbel probability density function (PDF) for value x using the parameters Mu and beta. For beta <= 0 the result is NAN.

Remarks:

With the standardized variable z = (x - Mu) / beta, the Gumbel probability density function is

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

Domain: x any real value, location Mu any real value, scale beta > 0. The Gumbel distribution is the limiting extreme-value distribution and a special case of the Generalized Extreme Value distribution. For beta <= 0 the result is NAN.

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

Overload 2: void GumbelPDF(TDenseMtxVec *X, double Mu, double beta, bool minimum, TDenseMtxVec *Res);

Gumbel distribution PDF (vectorized).

#NameTypeDescription
1XTDenseMtxVec *Defines distribution domain, real vector or matrix.
2MudoubleDefines the location parameter.
3betadoubleDefines the scale parameter, positive real value.
4minimumboolDefines maximum or minimum Gumbel distrubution. If true, th routine calculates minimum Gumbel PDF If false, the routine calculates maximum Gumbel PDF.
5ResTDenseMtxVec *After calculation stores the PDF 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