Double GenExtValueCDFInv(Double p, Double k, Double Mu, Double sigma)
Generalized extreme value (GEV) percent point function (PPF, quantile / inverse CDF).
| # | Name | Description |
|---|---|---|
| 1 | p | Probability, real value on the closed interval [0,1]. |
| 2 | k | Distribution shape parameter, real value. |
| 3 | Mu | Distribution location parameter, real value. |
| 4 | sigma | Distribution scale parameter, positive real value (sigma>0). |
Returns: Double - the value x such that GenExtValueCDF(x,k,Mu,sigma)=p, using shape k, location Mu and positive scale sigma. Returns NaN if sigma<=0 or p is outside [0,1].
Remarks:
The GEV inverse CDF has a closed form. With z defined below,
CDFInv(p | k,mu,sigma) = mu + sigma z , z = { ((-ln p)^(-k)-1)/k, if k != 0
{ [1.2ex] -ln(-ln p), if k=0 , 0 < p < 1 .
Boundary values: at p=0 or p=1 the result is mu-sigma/k or +/-inf according to the sign of k. Returns NaN for sigma<=0 or p outside [0,1].