Gamma2Sigma: Transformation of \(\Gamma\) matrix to \(\Sigma^{(k)}\) matrix
Description
Transforms the Gamma matrix from the definition of a
Huesler--Reiss distribution to the corresponding \(\Sigma^{(k)}\) matrix.
Usage
Gamma2Sigma(Gamma, k = 1, full = FALSE)
Value
Numeric \(\Sigma^{(k)}\) matrix of size \((d - 1) \times (d - 1)\) if
full = FALSE, and of size \(d \times d\) if full = TRUE.
Arguments
Gamma
Numeric \(d \times d\) variogram matrix.
k
Integer between 1 (the default value) and d.
Indicates which matrix \(\Sigma^{(k)}\) should be produced.
full
Logical. If true, then the kth row and column in \(\Sigma^{(k)}\)
are included and the function returns a \(d \times d\) matrix.
By default, full = FALSE.
Details
Every \(d \times d\) Gamma matrix in the definition of a
Huesler--Reiss distribution can be transformed into a
\((d - 1) \times (d - 1)\) \(\Sigma^{(k)}\) matrix,
for any k from 1 to d. The inverse of \(\Sigma^{(k)}\)
contains the graph structure corresponding to the Huesler--Reiss distribution
with parameter matrix Gamma. If full = TRUE, then \(\Sigma^{(k)}\)
is returned as a \(d \times d\) matrix with additional kth row and column
that contain zeros. For details see eng2019;textualgraphicalExtremes.
This is the inverse of function of Sigma2Gamma.