Double GenExtValueCDF(Double x, Double k, Double Mu, Double sigma)
Generalized extreme value (GEV) cumulative distribution function (CDF).
| # | 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 CDF 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:
With z=(x-mu)/sigma the Generalized Extreme Value CDF is
CDF(x | k,mu,sigma) = { exp[-(1+k z)^(-1/k)], if 1+k z > 0
{ [1.2ex] exp[-exp[-z]], if k=0 , z=(x-mu)/sigma .
The equivalent scipy.stats genextreme shape is . It is monotone non-decreasing. Returns NaN for sigma<=0, or when 1+k z <= 0 for k != 0.