ChiToGamma

Transform a \(\chi\) matrix to the corresponding variogram \(\Gamma\)

Usage

ChiToGamma(Chi_matrix)

Arguments

Chi_matrix

The matrix with \(\chi_{ij}\) entries.

Value

Gives the variogram \(\Gamma\) according to the \(\chi\) matrix for Hüsler-Reiss MGDP. In a such case, there exists a closed equation which link the variogram and the extremal coefficients, given by : $$ \chi_{ij} = 2 - 2 \phi(\sqrt{\Gamma_{ij}/2}) $$ where \(\phi\) is the standard normal distribution function.

Examples

ChiToGamma(matrix(c(1, 0.7,
                    0.7, 1),
           nrow = 2))
#>           [,1]      [,2]
#> [1,] 0.0000000 0.5938874
#> [2,] 0.5938874 0.0000000