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Statistics Seminar Series

Thursday, May 1, 2008 @ 4:00PM

425 Fenster Hall

New Jersey Institute of Technology

Shock Models, a Family of Discrete Laws and Corresponding Strongly Decreasing Failure Rate Laws in Continuous Time

Dr. M.C. Bhattacharjee

Department of Mathematical Sciences

New Jersey Institute of Technology

We explore a class of integer valued random variables defined via an integral representation of their p.g.f.s. Interest in and research on this problem is motivated by an apparently “surprising” connection between a class of classic “shock models” and the negatively aging notion of “strongly decreasing failure rate” (SDFR). A counterexample shows that there exist discrete distributions, having p.g.f.s with the desired integral representation, which do not have the discrete SDFR property, but can nevertheless induce a SDFR survival distribution in continuous time via shock models.