Extreme behavior of multivariate phase-type distributions

This paper investigates the limiting distributions of the componentwise 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 bivariate setup. For minima, it is shown that the dependence structure of the Marshall–Olkin class arises in the limit.