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

In POT: Generalized Pareto Distribution and Peaks Over Threshold

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)

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.

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]}

Value

A numeric vector.

Author(s)

Mathieu Ribatet

Examples

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

POT documentation built on Oct. 17, 2024, 5:06 p.m.