Exact Tail Asymptotics of Dirichlet Distributions

TL;DR

This paper derives exact asymptotic formulas for the tail probabilities of symmetrised Dirichlet random vectors in high dimensions, assuming their associated radii follow Gumbel max-domain distributions.

Contribution

It provides the first precise asymptotic expansion for tail probabilities of Dirichlet vectors under Gumbel domain assumptions.

Findings

Exact asymptotic expansion for tail probabilities derived

Applicable to high-dimensional Dirichlet distributions

Assumes Gumbel max-domain of attraction for the radius

Abstract

Let X be a generalised symmetrised Dirichlet random vector in R^k, and let u_n be thresholds such that P{X> u_n} tends to 0 as n goes infinity. In this paper we derive an exact asymptotic expansion of P{X> u_n} assuming that the associated random radius of X has distribution function in the Gumbel max-domain of attraction