Journal of Applied Probability

Concave renewal functions do not imply DFR interrenewal times

Yaming Yu

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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.

Article information

J. Appl. Probab. Volume 48, Number 2 (2011), 583-588.

First available in Project Euclid: 21 June 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K05: Renewal theory

Renewal theory log-convexity


Yu, Yaming. Concave renewal functions do not imply DFR interrenewal times. J. Appl. Probab. 48 (2011), no. 2, 583--588. doi:10.1239/jap/1308662647.

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