graphicalExtremes (version 0.1.0)

chi2Gamma: Transformation of extremal correlation \(\chi\) to the Huesler--Reiss variogram \(\Gamma\)

Description

Transforms the extremal correlation \(\chi\) into the Gamma matrix from the definition of a Huesler--Reiss distribution.

Usage

chi2Gamma(chi)

Value

Numeric or matrix. The \(\Gamma\) parameters in the Huesler--Reiss distribution.

Arguments

chi

Numeric or matrix, with entries between 0 and 1.

Details

The formula for transformation from chi to \(\Gamma\) that is applied element-wise is $$\Gamma = (2 \Phi^{-1}(1 - 0.5 \chi))^2,$$ where \(\Phi^{-1}\) is the inverse of the standard normal distribution function. This is the inverse of Gamma2chi.