LetH be the limiting distribution of a vector of maxima for ad-dimensional stationary sequnce with multivariate extremal index. We giv necessary and sufficient conditions forH to have independent or totally dependent margins by using relations between the multivariate extremal index and the univariate extremal indexes.

A new functional family of multivariates extreme value distributions, containingH, is introduced. We apply the results to characterize the asymptotic independence of the maximum and the minimum and compute the multivariate extremal index of the Multivariate Maxima of Moving Maxima process.

CEMAT - Center for Computational and Stochastic Mathematics