trans2UFrechet: Transformation to unit Frechet distribution
In ExtremalDep: Extremal Dependence Models

trans2UFrechet

R Documentation

Transformation to unit Frechet distribution

Description

Empirical and parametric transformation of a dataset to unit Frechet marginal distribution

Usage

trans2UFrechet(data, pars, type="Empirical")

Arguments

`data`	A vector of length `n` or a `(n \times p)` matrix representing the data on its original scale.
`pars`	A `(1 \times 3)` vector or a `(p \times 3)` matrix of marginal GEV parameters. Required when `type="GEV"`.
`type`	A character string indicating the type of transformation. Can take value `"Empirical"` or `"GEV"`.

Details

When type="Empirical", the transformation function is t(x)=-1/\log(F_{\textrm{emp}}(x)) where F_{\textrm{emp}}(x) denotes the empirical cumulative distribution.

When type="GEV", the transformation function is \left(1+\xi \frac{x-\mu}{\sigma}\right)^{1/\xi} if \xi \neq 0, \left( \frac{x-\mu}{\sigma}\right)^{-1} if \xi=0. If the argument pars is missing then a GEV is fitted on the columns of data using the fGEV function.

Value

An object of the same format and dimensions as data.

Author(s)

Simone Padoan, simone.padoan@unibocconi.it, https://faculty.unibocconi.it/simonepadoan/; Boris Beranger, borisberanger@gmail.com https://www.borisberanger.com;

Examples

data(MilanPollution)

pars <- fGEV(Milan.winter$PM10)$est
pars

data_uf <- trans2UFrechet(data=Milan.winter$PM10, pars=pars, 
                          type="GEV")
fGEV(data_uf)$est

data_uf2 <- trans2UFrechet(data=Milan.winter$PM10, 
                           type="Empirical")
fGEV(data_uf2)$est

ExtremalDep documentation built on Sept. 26, 2023, 1:06 a.m.