graphicalExtremes (version 0.1.0)

Gamma2chi: Transformation of the Huesler--Reiss variogram \(\Gamma\) to extremal correlation \(\chi\)

Description

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

Usage

Gamma2chi(Gamma)

Value

Numeric or matrix. The extremal correlation coefficient.

Arguments

Gamma

Numeric or matrix, with positive entries.

Details

The formula for transformation from Gamma to \(\chi\) that is applied element-wise is $$\chi = 2 - 2 \Phi(\sqrt{\Gamma} / 2),$$ where \(\Phi\) is the standard normal distribution function. This is the inverse of chi2Gamma.