Generalized Logistic Models and its orthant tail dependence

TL;DR

This paper introduces generalized multivariate logistic distributions using copula mixtures and stable variables, providing a flexible dependence structure and calculating tail dependence coefficients relevant for multivariate extreme value analysis.

Contribution

It extends classical logistic models to a more flexible family using copula mixtures and stable variables, and computes tail dependence coefficients.

Findings

Flexible dependence structure in generalized logistic models

Explicit computation of multivariate tail dependence coefficients

Extension of existing multivariate extreme value models

Abstract

The Multivariate Extreme Value distributions have shown their usefulness in environmental studies, financial and insurance mathematics. The Logistic or Gumbel-Hougaard distribution is one of the oldest multivariate extreme value models and it has been extended to asymmetric models. In this paper we introduce generalized logistic multivariate distributions. Our tools are mixtures of copulas and stable mixing variables, extending approaches in Tawn (1990), Joe and Hu (1996) and Foug\`eres et al. (2009). The parametric family of multivariate extreme value distributions considered presents a flexible dependence structure and we compute for it the multivariate tail dependence coefficients considered in Li (2009).