Max-min dependence coefficients for Multivariate Extreme Value Distributions

TL;DR

This paper introduces and analyzes the max-min dependence coefficient for multivariate extreme value distributions, linking it to tail dependence and extending it to multiple distributions, with practical illustrations.

Contribution

It defines a new dependence measure for multivariate extreme value distributions and extends it to multiple distributions, analyzing its properties and relationships.

Findings

Dependence measure relates to multivariate tail dependence.

Behavior under multivariate concordance ordering is characterized.

Illustrations with common distributions demonstrate the measure's application.

Abstract

We evaluate the dependence among the margins of a random vector with Multivariate Extreme Value distribution throughout the expected value of a range and relate this coefficient of dependence with the multivariate tail dependence. Its behaviour with respect to the multivariate concordance ordering is analysed. The definition of the min-max dependence coefficient is extended in order to evaluate the dependence among several multivariate extreme value distributions. The results are illustrated with some usual distributions.