Tail asymptotics of light-tailed Weibull-like sums

Abstract

TAIL ASYMPTOTICS OF LIGHT-TAILED WEIBULL-LIKE SUMSWe consider sums of n i.i.d. random variables with tailsclose to e xp{−x} for some > 1. Asymptotics developed by Rootzén 1987 and Balkema, Klüppelberg, and Resnick 1993 are discussed from the point of view of tails rather than of densities, using a some what differentangle, and supplemented with bounds, results on a random number N of terms, and simulation algorithms.