Probabilities.ErlangCDF Method

Overload List

#SignatureDescription
1procedure ErlangCDF(const X: TDenseMtxVec; k: Integer; Lambda: Double; const Res: TDenseMtxVec);Erlang CDF (vectorized).
2function ErlangCDF(x: Double; k: Integer; Lambda: Double): Double;Erlang cumulative distribution function (CDF).

Overload 1: procedure ErlangCDF(const X: TDenseMtxVec; k: Integer; Lambda: Double; const Res: TDenseMtxVec);

Erlang CDF (vectorized).

#NameDescription
1XDefines distribution domain, real vector or matrix with positive values or zero.
2kDefines distribution shape parameter. k must be a positive integer.
3LambdaDefines distribution rate parameter. Lambda must be a positive value.
4ResAfter calculation stores the CDF calculated from X, k and Lambda. 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: function ErlangCDF(x: Double; k: Integer; Lambda: Double): Double;

Erlang cumulative distribution function (CDF).

#NameDescription
1xFunction domain, real value >= 0.
2kShape parameter, integer > 0.
3LambdaRate parameter, real value > 0.

Returns: Double - the Erlang cumulative distribution function (CDF) at x for integer shape k and rate Lambda. Returns NAN when k <= 0 or Lambda <= 0.

Remarks:

Computes the Erlang CDF, the regularized lower incomplete gamma function:

CDF(x| k,lambda )= (gamma(k,lambda x))/((k-1)!) = P(k,lambda x)

The implementation evaluates it as GammaCDF(x, k, 1/Lambda). The result lies in [0,1][0,1] and is monotone non-decreasing. Domain: x >= 0, integer k > 0, lambda > 0. If k <= 0 or lambda <= 0 the result is NAN.

See Also: Probabilities.ErlangPDF, Probabilities.ErlangCDFInv