trans2UFrechet {ExtremalDep}

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, [e-mail], https://faculty.unibocconi.it/simonepadoan/; Boris Beranger, [e-mail] https://www.borisberanger.com;

See Also

trans2GEV, fGEV

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