A characterization of the rate of convergence in bivariate extreme value models (Q1871292)

Let \(G\) be a bivariate max-stable distribution function with reversed exponential margins. Define the bivariate generalized Pareto distribution correspondipg to \(G\) by \[ W(x,y)= 1+\log\bigl( G(x,y)\bigr),\quad \log\bigl( G(x,y)\bigr)\geq -1. \] The authors show that the rate of convergence of extremes in an iid sample of bivariate random vectors is determined by the distance of the underlying distribution from a bivariate generalized Pareto distribution.