Translator Disclaimer
June 2011 Concave renewal functions do not imply DFR interrenewal times
Yaming Yu
Author Affiliations +
J. Appl. Probab. 48(2): 583-588 (June 2011). DOI: 10.1239/jap/1308662647

Abstract

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.

Citation

Download Citation

Yaming Yu. "Concave renewal functions do not imply DFR interrenewal times." J. Appl. Probab. 48 (2) 583 - 588, June 2011. https://doi.org/10.1239/jap/1308662647

Information

Published: June 2011
First available in Project Euclid: 21 June 2011

zbMATH: 1219.60074
MathSciNet: MR2840319
Digital Object Identifier: 10.1239/jap/1308662647

Subjects:
Primary: 60K05

Keywords: Log-convexity , renewal theory

Rights: Copyright © 2011 Applied Probability Trust

JOURNAL ARTICLE
6 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.48 • No. 2 • June 2011
Back to Top