Probabilities.GumbelCDF Method

Overload List

#SignatureDescription
1void GumbelCDF(TDenseMtxVec X, Double Mu, Double beta, Boolean minimum, TDenseMtxVec Res)Gumbel distribution CDF (vectorized).
2Double GumbelCDF(Double x, Double Mu, Double beta, Boolean minimum)Gumbel cumulative distribution function (CDF).

Overload 1: void GumbelCDF(TDenseMtxVec X, Double Mu, Double beta, Boolean minimum, TDenseMtxVec Res)

Gumbel distribution CDF (vectorized).

#NameDescription
1XDefines distribution domain, real vector or matrix.
2MuDefines the location parameter.
3betaDefines the scale parameter, positive real value.
4minimumDefines maximum or minimum Gumbel distrubution. If true, the routine calculates minimum Gumbel PDF.
5ResAfter 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.

Result: stored in self (calling object)

Overload 2: Double GumbelCDF(Double x, Double Mu, Double beta, Boolean minimum)

Gumbel cumulative distribution function (CDF).

#NameDescription
1xFunction domain, real value.
2MuLocation parameter, real value.
3betaScale parameter, positive real value.
4minimumSelects the distribution sign. If true, the minimum (left) Gumbel CDF is computed
5if false, the maximum (right) Gumbel CDF.

Returns: Double - 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