Asymptotics for Kotz Type III Elliptical Distributions

TL;DR

This paper derives the tail asymptotics of Kotz Type III elliptical distributions, providing approximations for conditional excess distributions and insights into their asymptotic dependence properties.

Contribution

It introduces new asymptotic results for Kotz Type III elliptical distributions and applies these to approximate conditional excess distributions and analyze dependence.

Findings

Derived tail asymptotics for Kotz Type III distributions

Provided approximation methods for conditional excess distribution

Analyzed asymptotic dependence in Kotz Type III arrays

Abstract

In this paper we derive the tail asymptotics of a Kotz Type III elliptical random vector. As an application of our asymptotic expansion we derive an approximation for the conditional excess distribution. Furthermore, we discuss the asymptotic dependence of Kotz Type III triangular arrays and provide some details on the estimation of conditional excess distribution and survivor function.