ExtremalDep (version 1.0.0)

lambda.HR: Valid set of parameters for the 3-dimensional Husler-Reiss model

Description

Given two parameters of the Husler-Reiss model, this function evaluates the range of values the third parameter can take to ensure a positive definite matrix in the model.

Usage

lambda.HR(lambda)

Value

A \(2 \times 3\) matrix with, on the top, the lowest value of the parameter corresponding to the NA value in the input, and on the bottom the largest value.

Arguments

lambda

A vector of length 3 containing one NA and two positive values. The NA corresponds to the parameter for which the range is calculated.

Author

Simone Padoan, , https://faculty.unibocconi.it/simonepadoan/; Boris Beranger, , https://www.borisberanger.com.

Details

As indicated in Engelke et al. (2015), the matrix with zero diagonal and squared lambda parameters on the off-diagonal needs to be strictly conditionally negative definite.

References

Engelke, S., Malinowski, A., Kabluchko, Z., and Schlather, M. (2015). Estimation of Husler-Reiss distributions and Brown-Resnick processes. Journal of the Royal Statistical Society: Series B (Methodological), 77, 239--265.

Examples

ls <- lambda.HR(c(1, 2, NA))
dExtDep(
  x = c(0.1, 0.7, 0.2),
  method = "Parametric",
  model = "HR",
  par = ls[1, ],
  angular = TRUE
)