299 – Nonlinear Models and Other Optimization Problems
Example of a Renewal Process with No-Mean Inter-Arrival Times
Sponsor: Section on Statistical Computing
Keywords: renewal process, no-mean Pareto interarrivals, truncated Pareto interarrivals, finite-time and limiting probability distributions, integral equations, level crossing
Percy Brill
University of Windsor
Mei Ling Huang
Brock University
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.