Higher-order expansions of distributions of maxima in a H\"{u}sler-Reiss model

Abstract

The max-stable H\"usler-Reiss distribution which arises as the limit distribution of maxima of bivariate Gaussian triangular arrays has been shown to be useful in various extreme value models. For such triangular arrays, this paper establishes higher-order asymptotic expansions of the joint distribution of maxima under refined H\"{u}sler-Reiss conditions. In particular, the rate of convergence of normalized maxima to the H\"usler-Reiss distribution is explicitly calculated.