Concave Renewal Functions do not Imply DFR Interrenewal Times
Concave Renewal Functions do not Imply DFR Interrenewal Times
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 …