Probabilities::ErlangPDF Function

Probabilities Namespace

Overload List

#SignatureDescription
1double ErlangPDF(double x, int k, double Lambda);Erlang probability density function (PDF).
2void ErlangPDF(TDenseMtxVec *X, int k, double Lambda, TDenseMtxVec *Res);Erlang PDF (vectorized).

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

Erlang probability density function (PDF).

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

Returns: the Erlang probability density function (PDF) at x for integer shape k and rate Lambda. Returns NAN when k <= 0 or Lambda <= 0.

Remarks:

Computes the Erlang PDF

PDF(x| k,lambda )= (lambda ^k x^(k-1))/((k-1)!)* e^(-lambda x)

where k is an integer shape and lambda (Lambda) the rate. The Erlang distribution is the special case of the Probabilities::GammaPDF distribution with integer shape k and scale 1/lambda; for k=1 it reduces to the Probabilities::ExpPDF distribution. Domain: x >= 0, integer k > 0, lambda > 0. If k <= 0 or lambda <= 0 the result is NAN. A scalar form (this one) and a vectorized TDenseMtxVec overload are provided.

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

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

Erlang PDF (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 PDF 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