Concave Renewal Functions Do Not Imply DFR Inter-Renewal Times

Details Concave Renewal Functions Do Not Imply DFR Inter-Renewal Times Concave Renewal Functions Do Not Imply DFR Inter-Renewal Times

2010-09-13

arxiv.org/abs/1009.2463v1

Journal of Applied Probability 48 (2011) 583-588

Mathematics

Probability

8 pages, 1 figure

Scientific paper

10.1239/jap/1308662647

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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