chi2Gamma: Transformation between \eChi and \eGamma

In graphicalExtremes: Statistical Methodology for Graphical Extreme Value Models

Transformation between \eChi and \eGamma

Description

Transforms between the extremal correlation \eChi and the variogram \eGamma. Only valid for Huesler-Reiss distributions. Done element-wise, no checks of the entire matrix structure are performed.

Usage

chi2Gamma(chi)

Gamma2chi(Gamma)

Arguments

chi	Numeric vector or matrix with entries between 0 and 1.
Gamma	Numeric vector or matrix with non-negative entries.

Details

The formula for transformation from \eChi to \eGamma is element-wise

\Gamma = (2 \Phi^{-1}(1 - 0.5 \chi))^2,

where \Phi^{-1} is the inverse of the standard normal distribution function.

The formula for transformation from \eGamma to \eChi is element-wise

\chi = 2 - 2 \Phi(\sqrt{\Gamma} / 2),

where \Phi is the standard normal distribution function.

Value

Numeric vector or matrix containing the implied \eGamma.

Numeric vector or matrix containing the implied \eChi.

See Also

Other parameter matrix transformations: Gamma2Sigma(), Gamma2graph(), par2Matrix()

graphicalExtremes documentation built on Nov. 14, 2023, 1:07 a.m.