Example of a Renewal Process with No-Mean Inter-Arrival Times

• Activity Number: 299
• Type: Contributed
• Date/Time: Tuesday, August 5, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Computing
• Author(s): Percy Brill*+ and Mei Ling Huang
• Companies: University of Windsor and Brock University
• Keywords: renewal process ; no-mean Pareto interarrivals ; truncated Pareto interarrivals ; finite-time and limiting probability distributions ; integral equations ; level crossing

Abstract

We derive the finite-time t probability density function (pdf) of the excess, the age and the total life of a renewal process with interarrival times distributed as a no-mean Pareto distribution having shape parameter a? (0,1]. We compare the time-t pdf's with the corresponding limiting pdf's of a renewal process with interarrival times distributed as a finite-mean, truncated Pareto distribution having the same shape parameter a. The paper gives an example with fixed values t, a and right truncation point K, such that the limiting pdf's closely approximate the finite-time t pdf's on a subset of support.