Overload List
| # | Signature | Description |
|---|---|---|
| 1 | procedure GumbelPDF(const X: TDenseMtxVec; Mu: Double; beta: Double; minimum: Boolean; const Res: TDenseMtxVec); | Gumbel distribution PDF (vectorized). |
| 2 | function GumbelPDF(x: Double; Mu: Double; beta: Double; minimum: Boolean): Double; | Gumbel probability density function (PDF). |
Overload 1: procedure GumbelPDF(const X: TDenseMtxVec; Mu: Double; beta: Double; minimum: Boolean; const Res: TDenseMtxVec);
Gumbel distribution PDF (vectorized).
| # | Name | Description |
|---|---|---|
| 1 | X | Defines distribution domain, real vector or matrix. |
| 2 | Mu | Defines the location parameter. |
| 3 | beta | Defines the scale parameter, positive real value. |
| 4 | minimum | Defines maximum or minimum Gumbel distrubution. If true, th routine calculates minimum Gumbel PDF If false, the routine calculates maximum Gumbel PDF. |
| 5 | Res | After calculation stores the PDF calculated from X, Mu, and beta. 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 GumbelPDF(x: Double; Mu: Double; beta: Double; minimum: Boolean): Double;
Gumbel probability density function (PDF).
| # | Name | Description |
|---|---|---|
| 1 | x | Function domain, real value. |
| 2 | Mu | Location parameter, real value. |
| 3 | beta | Scale parameter, positive real value. |
| 4 | minimum | Selects the distribution sign. If true, the minimum (left/smallest) Gumbel PDF is computed |
| 5 | if false, the maximum (right/largest) Gumbel PDF. |
Returns: Double - the Gumbel probability density function (PDF) for value x using the parameters Mu and beta. For beta <= 0 the result is NAN.
Remarks:
With the standardized variable z = (x - Mu) / beta, the Gumbel probability density function is
PDF(x| mu,beta)={ 1/beta e^z e^(-e^z), if amp; minimum
{ [4pt] 1/beta e^(-z) e^(-e^(-z)), if amp; maximum
Domain: x any real value, location Mu any real value, scale beta > 0. The Gumbel distribution is the limiting extreme-value distribution and a special case of the Generalized Extreme Value distribution. For beta <= 0 the result is NAN.