The Asymptotics of Moments for the Remaining Time of Heavy-Tail Distributions

Abstract

Recent mathematical models of reliability computer systems and telecommunication networks are based on distributions with heavy tails. This paper falls into the category of exploring the classical models with heavy tails: Gnedenko–Weibull, Burr, Benktander distributions. The moment’s asymptotics for residual time have been derived especially for there heavy-tailed distributions. A simulation study is presented to give a practice characterization of the distributions with heavy tails.

Keywords

• heavy-tail distributions
• asymptotic expansion
• mean residual life function
• mean excess functions
• residual variance