On the structure of a family of probability generating functions induced by shock models
Abstract
We explore conditions for a class of functions defined via an integral representation to be a probability generating function of some positive integer valued random variable. Interest in and research on this question is motivated by an apparently surprising connection between a family of classic shock models due to Esary et. al. (1973) and the negatively aging nonparametric notion of ``strongly decreasing failure rate'' (SDFR) introduced by Bhattacharjee (2005). A counterexample shows that there exist probability generating functions with our integral representation which are not discrete SDFR, but when used as shock resistance probabilities can give rise to a SDFR survival distribution in continuous time.
Keywords
Cite
@article{arxiv.0805.2246,
title = {On the structure of a family of probability generating functions induced by shock models},
author = {Satrajit Roychoudhury and Manish C. Bhattacharjee},
journal= {arXiv preprint arXiv:0805.2246},
year = {2008}
}
Comments
Published in at http://dx.doi.org/10.1214/193940307000000536 the IMS Collections (http://www.imstat.org/publications/imscollections.htm) by the Institute of Mathematical Statistics (http://www.imstat.org)