Tail asymptotics of light-tailed Weibull-like sums

2017/12/11 by Asmussen, Søren, Hashorva, Enkelejd, Laub, Patrick J. +1
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1712.04070

Abstract

We consider sums of n i.i.d. random variables with tails close to exp\-x^β\ for some β>1. Asymptotics developed by Rootzén (1987) and Balkema, Klüppelberg & 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.

Related

• On Asymptotically Tight Tail Bounds for Sums of Geometric and Exponential Random Variables
• Asymptotic expansions for distributions of compound sums of light subexponential random variables
• Tail bounds for sums of geometric and exponential variables
• Tail Asymptotic of Sum and Product of Random Variables with Applications in the Theory of Extremes of Conditionally Gaussian Processes
• Tail probabilities of St. Petersburg sums, trimmed sums, and their limit