Asymptotics for Kotz Type III elliptical distributions

Let X be a Kotz Type III elliptical random vector in Rk,k≥2Rk,k≥2, and let tn,n≥1tn,n≥1 be positive constants such that limn→∞tn=∞limn→∞tn=∞. In this article we obtain an asymptotic expansion of P{X>tna},a∈Rk. As an application we derive an approximation for the conditional excess distribution and show the asymptotic dependence of Kotz Type III triangular arrays. Further, we provide some details on the estimation of conditional excess distributions and survivor function of Kotz Type III random vectors.