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WROCŁAW UNIVERSITY
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Contents of PMS, Vol. 37, Fasc. 2,
pages 235 - 256
 

TAIL ASYMPTOTICS OF LIGHT-TAILED WEIBULL-LIKE SUMS

Søren Asmussen
Enkelejd Hashorva
Patrick J. Laub
Thomas Taimre

Abstract: 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.

2010 AMS Mathematics Subject Classification: Primary: 62E20, 60F05; Secondary: 60E15, 65C05, 60F10.

Keywords and phrases: Gumbel MDA, Laplace transform, rare-event simulation, sums of of random variables, Weibull distribution.

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