Approximating the integrated tail distribution

Abstract

We propose a natural approximation for the estimation of the distribution function of an integrated tail distribution of a subexponential distribution and prove that the approximation is almost surely uniformly convergent. The behaviour of the approximating error is studied using simulation. Knowing the distribution function of an integrated tail distribution is useful in the context of GI/G/1 queue
with heavy-tailed service times and in the context of risk process with heavy-tailed claims.