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Concave Renewal Functions do not Imply DFR Interrenewal Times

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Yaming Yu
Yaming Yu*
Affiliation:
University of California
*
∗Postal address: Department of Statistics, University of California, Irvine, CA 92697, USA. Email address: [email protected]
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Abstract

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Brown (1980), (1981) proved that the renewal function is concave if the interrenewal distribution is DFR (decreasing failure rate), and conjectured the converse. This note settles Brown's conjecture with a class of counterexamples. We also give a short proof of Shanthikumar's (1988) result that the DFR property is closed under geometric compounding.

Keywords

Renewal theorylog-convexity

MSC classification

Secondary: 60K05: Renewal theory
Type
Research Article
Information
Journal of Applied Probability , Volume 48 , Issue 2 , June 2011 , pp. 583 - 588
Copyright
Copyright © Applied Probability Trust 2011 

References

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