Convergence rate to a lower tail dependence coefficient of a skew-t distribution

We examine the rate of decay to the limit of the tail dependence coefficient of a bivariate skew-t distribution. This distribution always displays asymptotic tail dependence. It contains as a special case the usual bivariate symmetric t distribution, and hence is an appropriate (skew) extension. The rate is asymptotically a power-law. The second-order structure of the univariate quantile function for such a skew-t distribution is a central issue. Our results generalise those for the bivariate symmetric t.