The data to be transformed to unit Frechet or ordinary GEV
margins
loc, scale, shape
The location, scale and shape parameters of
the GEV.
emp
Logical. If TRUE, data are transformed to unit
Frechet margins using the empirical CDF.
Value
Returns a numeric vector with the same length of x
Details
If Y is a random variable with a GEV distribution with location
\(\mu\), scale \(\sigma\) and shape
\(\xi\). Then,
$$Z = \left[1 + \xi \frac{Y - \mu}{\sigma} \right]_+^{1/\xi}$$
is unit Frechet distributed - where \(x_+ = \max(0, x)\).
If Z is a unit Frechet random variable. Then,
$$Y = \mu + \sigma \frac{Z_+^{\xi} - 1}{\xi}$$
is unit GEV distributed with location, scale and shape parameters
equal to \(\mu\), \(\sigma\) and \(\xi\)
respectively.