Probabilities::ErlangCDF Function

Overload List

#SignatureDescription
1double ErlangCDF(double x, int k, double Lambda);Erlang cumulative distribution function (CDF).
2void ErlangCDF(TDenseMtxVec *X, int k, double Lambda, TDenseMtxVec *Res);Erlang CDF (vectorized).

Overload 1: double ErlangCDF(double x, int k, double Lambda);

Erlang cumulative distribution function (CDF).

#NameTypeDescription
1xdoubleFunction domain, real value >= 0.
2kintShape parameter, integer > 0.
3LambdadoubleRate parameter, real value > 0.

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

Overload 2: void ErlangCDF(TDenseMtxVec *X, int k, double Lambda, TDenseMtxVec *Res);

Erlang CDF (vectorized).

#NameTypeDescription
1XTDenseMtxVec *Defines distribution domain, real vector or matrix with positive values or zero.
2kintDefines distribution shape parameter. k must be a positive integer.
3LambdadoubleDefines distribution rate parameter. Lambda must be a positive value.
4ResTDenseMtxVec *After 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.
Declared in Dew::Math::Units::Probabilities · Dew.Math/Units.Probabilities.h · Cross-compiler