Generating multivariate extreme value distributions

TL;DR

This paper introduces a new parametric family of multivariate extreme value distributions, deriving their copulas and dependence measures, and proposes a method to construct distributions with specified tail and extremal dependence properties.

Contribution

It provides a probabilistic framework for a flexible family of multivariate extreme value distributions with controllable dependence characteristics.

Findings

Derived the copula as a mixture of dependent and independent copulas.

Calculated bivariate tail dependence and extremal coefficients.

Proposed a method to construct distributions with desired tail/extremal coefficients.

Abstract

We define in a probabilistic way a parametric family of multivariate extreme value distributions. We derive its copula, which is a mixture of several complete dependent copulas and total independent copulas, and the bivariate tail dependence and extremal coefficients. Based on the obtained results for these coefficients, we propose a method to built multivariate extreme value distributions with prescribed tail/extremal coefficients. We illustrate the results with examples of simulation of these distributions.