Extremal properties of the multivariate extended skew-normal distribution

TL;DR

This paper investigates the extremal behavior of the multivariate extended skew-normal distribution, revealing asymptotic independence of maxima and deriving conditions for complex dependence structures in high dimensions.

Contribution

It provides new theoretical insights into the tail behavior and dependence structure of the multivariate extended skew-normal distribution, including asymptotic independence and extreme-value distribution approximation.

Findings

Multivariate maxima are asymptotically independent.

Derived the speed of convergence of the joint tail.

Established conditions for complex dependence structures.

Abstract

The skew-normal and related families are flexible and asymmetric parametric models suitable for modelling a diverse range of systems. We show that the multivariate maximum of a high-dimensional extended skew-normal random sample has asymptotically independent components and derive the speed of convergence of the joint tail. To describe the possible dependence among the components of the multivariate maximum, we show that under appropriate conditions an approximate multivariate extreme-value distribution that leads to a rich dependence structure can be derived.