Bivariate distributions with given extreme value attractor

A new class of bivariate distributions is introduced and studied, which enc ompasses Archimedean copulas and extreme value distributions as special cas es. Its dependence structure is described, its maximum and minimum attracto rs are determined, and an algorithm is given for generating observations fr om ally member of this class. It is also shown how it is possible to constr uct distributions in this family with a predetermined extreme value attract or. This construction is used to study via simulation the small-sample beha vior of a bivariate threshold method suggested by H. Joe, R. L. Smith, and I. Weissman (1992, J. Roy. Statist. Soc. Ser. B 54, 171-183) for estimating the joint distribution of extremes of two random variates. (C) 2000 Academ ic Press. AMS 1991 subject classifications: 62H05, 60G70, 62G05.