Bivariate extreme value theory: Models and estimation

TLDR

Bivariate extreme value distributions arise as limits of renormalized componentwise maxima, yet no natural parametric family captures the dependence between marginals, although restrictions exist. The study proposes two new parametric models for the dependence function in bivariate extreme value distributions. The authors develop these two parametric dependence models and provide tests for independence and model discrimination. The estimation procedure and model flexibility are demonstrated using sea level data.

Abstract

Bivariate extreme value distributions arise as the limiting distributions of renormalized componentwise maxima. No natural parametric family exists for the dependence between the marginal distributions, but there are considerable restrictions on the dependence structure. We consider modelling the dependence function with parametric models, for which two new models are presented. Tests for independence, and discriminating between models, are also given. The estimation procedure, and the flexibility of the new models, are illustrated with an application to sea level data.