A novel class of bivariate max-stable distributions

In this paper we consider bivariate triangular arrays given in terms of linear transformations of asymptotically spherical bivariate random vectors. We show under certain restrictions that the componentwise maxima of such arrays is attracted by a bivariate max-stable distribution function with three parameters. This new class of max-stable distributions includes the bivariate max-stable Hüsler–Reiss distribution function for a special choice of parameters.