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.
Arguments
- chi
Numeric vector or matrix with entries between 0 and 1.
- Gamma
Numeric vector or matrix with non-negative entries.
Value
Numeric vector or matrix containing the implied \(\Gamma\).
Numeric vector or matrix containing the implied \(\chi\).
Details
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.
See also
Other parameter matrix transformations:
Gamma2Sigma(),
Gamma2graph(),
par2Matrix()