dim_ExtDep {ExtremalDep}

Dimensions calculations for parametric extremal dependence models

Description

This function calculates the dimensions of an extremal dependence model for a given set of parameters, the dimension of the parameter vector for a given dimension and verifies the adequacy between model dimension and length of parameter vector when both are provided.

Usage

dim_ExtDep(model, par=NULL, dim=NULL)

Arguments

model

A string with the name of the model: "PB" (Pairwise Beta), "HR" (Husler-Reiss), "ET" (Extremal-t), "EST" (Extremal Skew-t), TD (Tilted Dirichlet) or AL (Asymmetric Logistic).

par

A vector representing the parameters of the model.

dim

An integer representing the dimension of the model.

Details

One of par or dim need to be provided. If par is provided, the dimension of the model is calculated. If dim is provided, the length of the parameter vector is calculated. If both par and dim are provided, the adequacy between the dimension of the model and the length of the parameter vector is checked.

For model="HR", the parameter vector is of length choose(dim,2). For model="PB" or model="Extremalt", the parameter vector is of length choose(dim,2) + 1. For model="EST", the parameter vector is of length choose(dim,2) + dim + 1. For model="TD", the parameter vector is of length dim. For model="AL", the parameter vector is of length 2^(dim-1)*(dim+2) - (2*dim+1).

Value

If par is not provided and dim is provided: returns an integer indicating the length of the parameter vector. If par is provided and dim is not provided: returns an integer indicating the dimension of the model. If par and dim are provided: returns a TRUE/FALSEstatement indicating whether the length of the parameter and the dimension match.

Author(s)

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

Examples

  dim_ExtDep(model="EST", dim=3)
  dim_ExtDep(model="AL", dim=3)
  
  dim_ExtDep(model="PB", par=rep(0.5,choose(4,2)+1) )
  dim_ExtDep(model="TD", par=rep(1,5) )
  
  dim_ExtDep(model="EST", dim=2, par=c(0.5,1,1,1) )
  dim_ExtDep(model="PB", dim=4, par=rep(0.5,choose(4,2)+1) )