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

In ExtremalDep: Extremal Dependence Models

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)

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.

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.

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.

Author(s)

Simone Padoan, [e-mail], https://faculty.unibocconi.it/simonepadoan/; Boris Beranger, [e-mail], https://www.borisberanger.com.

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
)

ExtremalDep documentation built on Aug. 21, 2025, 5:57 p.m.