trans2UFrechet: Transformation to Unit Frechet Distribution

In ExtremalDep: Extremal Dependence Models

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 be "Empirical" or "GEV".

Details

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

When type = "GEV", the transformation is \left(1 + \xi \frac{x-\mu}{\sigma}\right)^{1/\xi} if \xi \neq 0, and \sigma / (x-\mu) if \xi = 0. If pars is missing, 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

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 Aug. 21, 2025, 5:57 p.m.