graphicalExtremes (version 0.2.0)

Gamma2Theta: Transformation of \(\Gamma\) matrix to \(\Theta\) matrix

Description

Transforms the variogram matrix (\(\Gamma\)) from the definition of a Huesler--Reiss distribution to the corresponding precision matrix (\(\Theta\) or \(\Theta^k\)).

Usage

Gamma2Theta(Gamma, k = NULL)

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

NULL or integer between 1 and d. If this is NULL, the \(d \times d\) matrix \(\Theta\) is produced, otherwise the specified \((d-1) \times (d-1)\) matrix \(\Theta^k\).

Details

Every \(d \times d\) Gamma matrix in the definition of a Huesler--Reiss distribution can be transformed into a \(d \times d\) \(\Theta\) matrix, which contains the graph structure corresponding to the Huesler--Reiss distribution with parameter matrix Gamma.

References

See Also

Other MatrixTransformations: Gamma2Sigma(), Gamma2graph(), Sigma2Gamma(), Theta2Gamma()

Examples

Gamma <- cbind(
  c(0, 1.5, 1.5, 2),
  c(1.5, 0, 2, 1.5),
  c(1.5, 2, 0, 1.5),
  c(2, 1.5, 1.5, 0)
)
Gamma2Theta(Gamma)