On the structure of a family of probability generating functions induced by shock models

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dc.creatorRoychoudhury, Satrajit
dc.creatorBhattacharjee, Manish C.
dc.date2008-05-15
dc.date.accessioned2026-07-07T12:18:54Z
dc.date.available2026-07-07T12:18:54Z
dc.descriptionWe 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.
dc.descriptionPublished 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)
dc.identifierhttps://arxiv.org/abs/0805.2246
dc.identifierhttp://arxiv.org/abs/0805.2246
dc.identifierIMS Collections 2008, Vol. 1, 78-88
dc.identifierdoi:10.1214/193940307000000536
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/212573
dc.subjectStatistics Theory
dc.subject60K10 (Primary) 90B25 (Secondary)
dc.titleOn the structure of a family of probability generating functions induced by shock models
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