Extreme Behavior of Multivariate Phase-Type Distributions

Abstract

This paper investigates the limiting distributions of the component-wise maxima and minima of suitably normalized iid multivariate phase-type random vectors. In the case of maxima, a large parametric class of multivariate extreme value (MEV) distributions is obtained. The flexibility of this new class is exemplified in the bi-variate setup. For minima, it is shown that the dependence structure of the Marshall-Olkin class arises in the limit.

Keywords: component-wise maxima (minima), copula, Marshall-Olkin exponential distribution, multivariate extreme value distribution, Pickands’ representation

JEL Classification: C10, C60