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arXiv · 1009.2463

Concave Renewal Functions Do Not Imply DFR Inter-Renewal Times

Yaming Yu
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Abstract

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

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Yaming Yu. 2010-09-13. Concave Renewal Functions Do Not Imply DFR Inter-Renewal Times. https://doi.org/10.1239/jap/1308662647

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