gev2frech {SpatialExtremes} | R Documentation |
Transforms GEV data to unit Frechet ones and vice versa
Description
Transforms GEV data to unit Frechet ones and vice versa
Usage
gev2frech(x, loc, scale, shape, emp = FALSE)
frech2gev(x, loc, scale, shape)
Arguments
x |
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 |
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.
Value
Returns a numeric vector with the same length of x
Author(s)
Mathieu Ribatet
Examples
x <- c(2.2975896, 1.6448808, 1.3323833, -0.4464904, 2.2737603,
-0.2581876, 9.5184398, -0.5899699, 0.4974283, -0.8152157)
y <- gev2frech(x, 1, 2, .2)
y
frech2gev(y, 1, 2, .2)
[Package SpatialExtremes version 2.1-0 Index]