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Probabilities.ErlangPDF Method (double, int, double)
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Erlang probability density function (PDF).

Syntax
C#
Visual Basic
public static double ErlangPDF(double x, int k, double Lambda);
Parameters
Parameters 
Description 
double x 
Function domain, real positive value or zero. 
int k 
Defines distribution shape parameter. k must be a positive integer. 
double 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.

Remarks

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.

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