Tail Asymptotics and Estimation for Elliptical Distributions

TL;DR

This paper derives second order asymptotic expansions for the joint survival probability of bivariate elliptical distributions with radii in the Gumbel max-domain, aiding statistical modeling of extreme events.

Contribution

It provides a second order asymptotic expansion for joint survival probabilities in elliptical distributions, enhancing understanding of tail behavior in multivariate extremes.

Findings

Second order asymptotic expansion for P(X > x, Y > y)

Insights into statistical modeling of joint survival probabilities

Discussion on survival conditional excess probability

Abstract

Let (X,Y) be a bivariate elliptical random vector with associated random radius in the Gumbel max-domain of attraction. In this paper we obtain a second order asymptotic expansion of the joint survival probability P(X > x, Y> y) for x,y large. Further, based on the asymptotic bounds we discuss some aspects of the statistical modelling of joint survival probabilities and the survival conditional excess probability.