Comparison results and aging properties of geometric counting processes

A. Di Crescenzo, F. Pellerey

We deal with counting processes having geometrically distributed increments, which can be obtained as suitable Mixed Poisson processes. We discuss various comparison results and aging properties concerning total claim amounts and random lifetimes for shock models and compound counting models whose shocks and claims occur according to geometric counting processes. Furthermore, we face the first-crossing-time problem through various types of boundaries, and present several applications.

Keywords: Counting processes Multivariate geometric distribution First-crossing time Shock models Stochastic orders Aging

M. C. López Díaz, M. Lopez Diaz, S. Martínez

F. G. Badía Blasco