Transforms between the extremal correlation \(\chi\) and the variogram \(\Gamma\). Only valid for Huesler-Reiss distributions. Done element-wise, no checks of the entire matrix structure are performed.
chi2Gamma(chi)Gamma2chi(Gamma)
Numeric vector or matrix containing the implied \(\Gamma\).
Numeric vector or matrix containing the implied \(\chi\).
Numeric vector or matrix with entries between 0 and 1.
Numeric vector or matrix with non-negative entries.
The formula for transformation from \(\chi\) to \(\Gamma\) 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 \(\Gamma\) to \(\chi\) is element-wise $$\chi = 2 - 2 \Phi(\sqrt{\Gamma} / 2),$$ where \(\Phi\) is the standard normal distribution function.
Other parameter matrix transformations:
Gamma2Sigma(),
Gamma2graph(),
par2Matrix()