SpatialExtremes (version 2.0-0)

gev2frech: 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 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.

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)