A class of multivariate extreme value distributions with heterogeneous margins

Many problems which involve applications of extreme value theory show an essential multivariate nature and recent development of the theory in this field deal with the construction of multivariate extreme value distributions. Owing to the nature of the problem under examination, extreme values to be analyzed jointly may have different limiting distributions, but it seems that explicit expressions of multivariate extreme value distributions with heterogeneous margins are not present in the literature. In this paper we consider the problem of constructing multivariate extreme value distributions with univariate marginal extreme value distributions not belonging or, more generally, not all belonging, to the same type, and introduce a class of distributions of this kind. The construction procedure proposed in the paper is based on the marginal transformation method. We point out that the marginal distributions, of any order, associated to a generic k-dimensional distribution of this class, are of the same form as the k-dimensional distribution. Finally we provide an example of trivariate extreme value distribution with margins of three different types.