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Tail asymptotics of light-tailed Weibull-like sums

Asmussen S., Hashorva E., Laub P. J., Taimre T.

Probability and Mathematical Statistics

2017

Vol. 37, Fasc. 2

235--256

We consider sums of n i.i.d. random variables with tails close to exp{−xβ} for some β > 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 somewhat different angle, and supplemented with bounds, results on a random number N of terms, and simulation algorithms.