Probabilities.ErlangPDF Function

Erlang probability density function (PDF).

Pascal

function ErlangPDF(x: double; k: Integer; Lambda: double): double; overload;

Parameters	Description
x	Function domain, real positive value or zero.
k	Defines distribution shape parameter. k must be a positive integer.
Lambda	Defines distribution rate parameter. Lambda must be a positive value.

Returns

the Erlang probability density function (PDF) for integer parameter k and double parameter Lambda at the value x. Parameters k and Lambda must both be greater than zero.

Description

The Erlang probability distribution function (PDF) is defined by the following relation:

The Erlang distribution is a continuous distribution, which has a positive value for all real numbers greater than zero, and is given by two parameters: the shape k, which is an integer, and the rate Lambda, which is a real. The distribution is sometimes defined using the inverse of the rate parameter, the scale phi. When the shape parameter k equals 1, the distribution simplifies to the exponential distribution.

The Erlang distribution is a special case of the Gamma distribution where the shape parameter k is an integer. In the Gamma distribution, this parameter is a real.