Summary
Erlang probability density function (PDF).Unit
Probabilities
Declaration
Procedure ErlangPDF(X: TDenseMtxVec; k: Integer; lambda: TSample; Res: TDenseMtxVec);
Description
Calculates the Erlang PDF for vector X using the parameters k and lambda. The results are stored in vector Res. The Res Length and Complex properties are adjusted automatically. If vector X is complex, an exception is raised.Declaration
Function ErlangPDF(x: TSample; k: Integer; lambda: TSample): TSample;
| Parameter | Description |
|---|---|
| x | Defines distribution parameter, valid on [0,INF) interval. |
| k | Defines distribution shape parameter. k must be a positive integer. |
| lambda | Defines distribution rate parameter. Lambda must be a positive value. |
Result
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
Calculates the Erlang probability distribution function, 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.
Parameters:
- k: (1,2,3...)
- lambda: (0,INF)
Categories
Continuous probabilities| See Also |
|---|
| ErlangCDF |
| ErlangCDFInv |
| Copyright 2008 Dew Research |