graphicalExtremes (version 0.1.0)

Sigma2Gamma: Transformation of \(\Sigma^{(k)}\) matrix to \(\Gamma\) matrix

Description

Transforms the \(\Sigma^{(k)}\) matrix from the definition of a Huesler--Reiss distribution to the corresponding \(\Gamma\) matrix.

Usage

Sigma2Gamma(S, k = 1, full = FALSE)

Value

Numeric \(d \times d\)

\(\Gamma\) matrix.

Arguments

S

Numeric \((d - 1) \times (d - 1)\) covariance matrix \(\Sigma^{(k)}\) from the definition of a Huesler--Reiss distribution. Numeric \(d \times d\) covariance matrix if full = TRUE, see full parameter.

k

Integer between 1 (the default value) and d. Indicates which matrix \(\Sigma^{(k)}\) is represented by S.

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

For any k from 1 to d, the \(\Sigma^{(k)}\) matrix of size \((d - 1) \times (d - 1)\) in the definition of a Huesler--Reiss distribution can be transformed into a the corresponding \(d \times d\) \(\Gamma\) matrix. If full = TRUE, then \(\Sigma^{(k)}\) must be a \(d \times d\) matrix with kth row and column containing zeros. For details see eng2019;textualgraphicalExtremes. This is the inverse of function of Gamma2Sigma.

References

Examples

Sigma1 <-  rbind(c(1.5, 0.5, 1),
                 c(0.5, 1.5, 1),
                 c(1, 1, 2))
Sigma2Gamma(Sigma1, k = 1, full = FALSE)