Overload List
| # | Signature | Description |
|---|---|---|
| 1 | procedure ErlangCDF(const X: TDenseMtxVec; k: Integer; Lambda: Double; const Res: TDenseMtxVec); | Erlang CDF (vectorized). |
| 2 | function ErlangCDF(x: Double; k: Integer; Lambda: Double): Double; | Erlang cumulative distribution function (CDF). |
Overload 1: procedure ErlangCDF(const X: TDenseMtxVec; k: Integer; Lambda: Double; const Res: TDenseMtxVec);
Erlang CDF (vectorized).
| # | Name | Description |
|---|---|---|
| 1 | X | Defines distribution domain, real vector or matrix with positive values or zero. |
| 2 | k | Defines distribution shape parameter. k must be a positive integer. |
| 3 | Lambda | Defines distribution rate parameter. Lambda must be a positive value. |
| 4 | Res | After calculation stores the CDF 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: function ErlangCDF(x: Double; k: Integer; Lambda: Double): Double;
Erlang cumulative distribution function (CDF).
| # | Name | Description |
|---|---|---|
| 1 | x | Function domain, real value >= 0. |
| 2 | k | Shape parameter, integer > 0. |
| 3 | Lambda | Rate parameter, real value > 0. |
Returns: Double - the Erlang cumulative distribution function (CDF) at x for integer shape k and rate Lambda. Returns NAN when k <= 0 or Lambda <= 0.
Remarks:
Computes the Erlang CDF, the regularized lower incomplete gamma function:
CDF(x| k,lambda )= (gamma(k,lambda x))/((k-1)!) = P(k,lambda x)
The implementation evaluates it as GammaCDF(x, k, 1/Lambda). The result lies in and is monotone non-decreasing. Domain: x >= 0, integer k > 0, lambda > 0. If k <= 0 or lambda <= 0 the result is NAN.