Multivariate Negative Exponential and Extreme Value Distributions

Abstract

We survey multivariate extreme value distributions. These are limiting distributions of maxima and/or minima, componentwise, after suitable normalization. A distribution is extreme value stable if and only if its margins are stable and its dependence function is stable. Thus it is possible, without loss of generality, to choose any stable marginal distribution deemed convenient. We use the negative exponential one. The class of multivariate stable negative exponential distributions is characterized by the fact that weighted minima of components have negative exponential distributions. We examine several representations and the relationships among them and we consider, in terms of them, joint densities and scalar measures of dependence. We also consider estimation.