Tail dependence functions of the bivariate Hüsler–Reiss model

Abstract

The tail dependence coefficient, a special case of the tail dependence function, measures extremal dependence between two random variables. It is known that the tail dependence coefficient of bivariate Gaussian random vectors with constant correlation coefficient |ρ|<1 is zero with rate satisfying regular variation at zero. In this note, we consider the tail dependence function of bivariate Gaussian random vectors with dynamic correlation coefficient ρn satisfying the Hüsler–Reiss condition. We also establish the convergence rates to the tail dependence functions under some refined Hüsler–Reiss conditions. By-products are the tail orders and tail order functions with related expansions.