Multivariate Extremal Models Under Non-Classical Situations

Emilia Athayde and M. Ivette Gomes
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Emilia Athayde: Center of Statistics and Applications (I.N.I.C.)
M. Ivette Gomes: Center of Statistics and Applications (I.N.I.C.)

A chapter in Mathematical Statistics and Probability Theory, 1987, pp 1-9 from Springer

Abstract: 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 Xk’s with distribution function Fk(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.

Date: 1987
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DOI: 10.1007/978-94-009-3965-3_1

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