Multivariate Extremal Models Under Non-Classical Situations

Abstract

The limiting distribution of top order statistics in a non-classical set-up, where the independence structure remains valid, is reviewed in this paper. We essentially place ourselves under Mejzler’s hypothesis — independent X_k’s with distribution function F_k(x), k ^≥1, satisfying the uniformity condition for the maximum. Notice that the results presented are obviously valid not only on Mejzler’s M ₁ class, but also on refinements M _r, r>1, of Mejzler’s class and in ${M_\infty } = \bigcap\limits_{r \geqslant 1} {{M_r}}$, a non-trivial extension of the class S of max-stable distributions. Generalizing the multivariate GEV model, other multivariate extremal models based on functions H(x) belonging to M ₁ (or to M _∞) are introduced and inference techniques are developed for a multivariate extremal Pareto model.