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

Satrajit Roychoudhury and Manish C. Bhattacharjee

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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.

Chapter information

Source
N. Balakrishnan, Edsel A. Peña and Mervyn J. Silvapulle, eds., Beyond Parametrics in Interdisciplinary Research: Festschrift in Honor of Professor Pranab K. Sen (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2008), 78-88

Dates
First available in Project Euclid: 1 April 2008

Permanent link to this document
https://projecteuclid.org/euclid.imsc/1207058265

Digital Object Identifier
doi:10.1214/193940307000000536

Mathematical Reviews number (MathSciNet)
MR2462200

Subjects
Primary: 60K10: Applications (reliability, demand theory, etc.)
Secondary: 90B25: Reliability, availability, maintenance, inspection [See also 60K10, 62N05]

Keywords
Esary-Marshall-Proschan shock model strong DFR

Rights
Copyright © 2008, Institute of Mathematical Statistics

Citation

Roychoudhury, Satrajit; Bhattacharjee, Manish C. On the structure of a family of probability generating functions induced by shock models. Beyond Parametrics in Interdisciplinary Research: Festschrift in Honor of Professor Pranab K. Sen, 78--88, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2008. doi:10.1214/193940307000000536. https://projecteuclid.org/euclid.imsc/1207058265


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References

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