Multivariate extremes of generalized skew-normal distributions

We explore extremal properties of a family of skewed distributions extended from the multivariate normal distribution by introducing a skewing function π. We give sufficient conditions on the skewing function for the pairwise asymptotic independence to hold. We apply our results to a special case of the bivariate skew-normal distribution and finally support our conclusions by a simulation study which indicates that the rate of convergence is quite slow.