POT (version 1.1-11)

gpd2frech: Transforms GPD Observations to Unit Frechet Ones and Vice Versa

Description

Transforms GPD observations to unit Frechet ones and vice versa

Usage

gpd2frech(x, loc = 0, scale = 1, shape = 0, pat = 1)
frech2gpd(z, loc = 0, scale = 1, shape = 0, pat = 1)

Value

A numeric vector.

Arguments

x,z

The vector of observations.

loc,scale,shape

The location, scale and shape parameters respectively.

pat

The proportion above the threshold, i.e. Pr[X > log] = pat.

Author

Mathieu Ribatet

Details

Let \(x_i\), \(i=1,\ldots,n\) be the realisation of a GPD random variable. Thus, the transformation to unit Frechet is defined as:

$$z_i = - \frac{1}{\log\left[1 - pat \left(1 + shape \frac{x_i - loc}{scale}\right)_+^{-1/shape}\right]}$$

Examples

x <- rgpd(10, 0, 1, 0.25)
z <- gpd2frech(x, 0, 1, 0.25)
z
all(frech2gpd(z, 0, 1, 0.25) == x)