R: Transforms GEV data to unit Frechet ones and vice versa

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 `TRUE`, data are transformed to unit Frechet margins using the empirical CDF.

### Details

If Y is a random variable with a GEV distribution with location μ, scale σ and shape ξ. Then,

Z = [1 + ξ (Y - μ) / σ]_+^(1/ξ)

is unit Frechet distributed - where x_+ = max(0, x).

If Z is a unit Frechet random variable. Then,

Y = μ + σ (Z_+^(ξ) - 1) / ξ

is unit GEV distributed with location, scale and shape parameters equal to μ, σ and ξ 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 2.0-5 Index]