Tail asymptotics of light-tailed Weibull-like sums

By Søren Asmussen, Enkelejd Hashorva, Patrick J. Laub and Thomas Taimre
Thiele Research Reports
No. 04, March 2017
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.

Keywords: Gumbel MDA; Laplace transform; Rare event simulation; Sums of of random variables; Weibull distribution

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