Probabilities.ErlangPDF Method

Overload List

#SignatureDescription
1void ErlangPDF(TDenseMtxVec X, Int32 k, Double Lambda, TDenseMtxVec Res)Erlang PDF (vectorized).
2Double ErlangPDF(Double x, Int32 k, Double Lambda)Erlang probability density function (PDF).

Overload 1: void ErlangPDF(TDenseMtxVec X, Int32 k, Double Lambda, TDenseMtxVec Res)

Erlang PDF (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 PDF 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: Double ErlangPDF(Double x, Int32 k, Double Lambda)

Erlang probability density function (PDF).

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

Returns: Double - 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 Dew.Math.Units.Probabilities.GammaPDF distribution with integer shape k and scale 1/lambda; for k=1 it reduces to the Dew.Math.Units.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 Dew.Math.TDenseMtxVec overload are provided.

See Also: Probabilities.ErlangCDF, Probabilities.ErlangCDFInv