Tail dependence convergence rate for the bivariate skew normal under the equal-skewness condition

Abstract

We derive the rate of decay of the tail dependence of the bivariate skew normal distribution under the equal-skewness condition {\theta}1 = {\theta}2,= {\theta}, say. The rate of convergence depends on whether {\theta} > 0 or {\theta} < 0. The latter case gives rate asymp- totically identical with the case {\theta} = 0. The asymptotic behaviour of the quantile function for the univariate skew normal is part of the theoretical development.