Multivariate multiparameter extreme value models and return periods: A copula approach

Abstract

Multivariate extreme value models are a fundamental tool in order to assess potentially dangerous events. The target of this paper is two‐fold. On the one hand we outline how, exploiting recent theoretical developments in the theory of copulas, new multivariate extreme value distributions can be easily constructed; in particular, we show how a suitable number of parameters can be introduced, a feature not shared by traditional extreme value models. On the other hand, we introduce a proper new definition of multivariate return period and show the differences with (and the advantages over) the definition presently used in literature. An illustration involving flood data is presented and discussed, and a generalization of the well‐known multivariate logistic Gumbel model is also given.