Tail asymptotics for the bivariate skew normal

We derive the asymptotic rate of decay to zero of the tail dependence of the bivariate skew normal distribution under the equal-skewness condition α₁=α₂, =α, say. The rate depends on whether α>0 or α<0. For the lower tail, the latter case has rate asymptotically identical with the bivariate normal (α=0), but has a different multiplicative constant. The case α>0 gives a rate dependent on α. The detailed asymptotic behaviour of the quantile function for the univariate skew normal is a key. This study is partly a sequel to our earlier one on the analogous situation for bivariate skew t.