Products in Conditional Extreme Value Model

TL;DR

This paper investigates the behavior of the product of components in a conditional extreme value model, expanding the understanding of extremal dependence when one component is in the Fréchet or Weibull domain.

Contribution

It introduces an analysis of the product of components within a conditional extreme value framework, extending previous models to include Fréchet and Weibull domains.

Findings

Characterizes the distribution of products under the model.

Provides conditions for asymptotic dependence and independence.

Extends the theory of conditional extreme value models.

Abstract

The classical multivariate extreme value theory tries to capture the extremal dependence between the components under a multivariate domain of attraction condition and it requires each of the components to be in the domain of attraction of a univariate extreme value distribution as well. The multivariate extreme value (MEV) model has a rich theory but has some limitations as it fails to capture the dependence structure in presence of asymptotic independence. A different approach to MEV was given by Heffernan and Tawn (2004), where they examined MEV distributions by conditioning on one of the components to be extreme. Here we assume one of the components to be in Frech\'et or Weibull domain of attraction and study the behavior of the product of the components under this conditional extreme value model.