function GenExtValuePDF(x: Double; k: Double; Mu: Double; sigma: Double): Double;
Generalized extreme value (GEV) probability density function (PDF).
| # | Name | Description |
|---|---|---|
| 1 | x | Distribution domain, real value |
| 2 | valid when k*(x-Mu)/sigma > -1. | |
| 3 | k | Distribution shape parameter, real value. |
| 4 | Mu | Distribution location parameter, real value. |
| 5 | sigma | Distribution scale parameter, positive real value (sigma>0). |
Returns: Double - the Generalized extreme value PDF for value x using shape k, location Mu and positive scale sigma. Returns NaN if sigma<=0, or (for k<>0) if 1+k(x-Mu)/sigma<=0.
Remarks:
Calculates the Generalized extreme value density. With z=(x-mu)/sigma,
PDF(x | k,mu,sigma) = { 1/sigma(1+k z)^(-1/k-1) exp[-(1+k z)^(-1/k)], if 1+k z > 0
{ [1.2ex] 1/sigmaexp[-exp[-z]-z], if k=0 , z=(x-mu)/sigma .
This shape convention uses (1+k z)^(-1/k); the equivalent scipy.stats genextreme shape is . Returns NaN for sigma<=0, or when 1+k z <= 0 for k != 0.