Multivariate extreme models based on underlying skew-tt and skew-normal distributions

We derive for the first time the limiting distribution of maxima of skew-tt random vectors and we show that its limiting case, as the degree of freedom goes to infinity, is the skewed version of the well-known Hüsler–Reiss model. The advantage of the new families of models is that they are particularly flexible, allowing for both symmetric and asymmetric dependence structures and permitting the modelling of multivariate extremes with dimensions greater than two.