Tail asymptotics of light-tailed Weibull-like sums

TL;DR

This paper investigates the tail behavior of sums of i.i.d. light-tailed Weibull-like random variables, providing new bounds, insights on the random number of terms, and simulation methods.

Contribution

It offers a novel perspective on tail asymptotics for Weibull-like sums, extending previous work with bounds, analysis of random summation, and simulation techniques.

Findings

Derived bounds for tail probabilities

Analyzed sums with random number of terms

Developed simulation algorithms for tail estimation

Abstract

We consider sums of $n$ i.i.d. random variables with tails close to $\exp\{-x^\beta\}$ for some $\beta>1$. Asymptotics developed by Rootz\'en (1987) and Balkema, Kl\"uppelberg & Resnick (1993) are discussed from the point of view of tails rather of densities, using a somewhat different angle, and supplemented with bounds, results on a random number $N$ of terms, and simulation algorithms.