Open Access
Translator Disclaimer
October, 1981 Further Monotonicity Properties for Specialized Renewal Processes
Mark Brown
Ann. Probab. 9(5): 891-895 (October, 1981). DOI: 10.1214/aop/1176994317

Abstract

Define $Z(t)$ to be the forward recurrence time at $t$ for a renewal process with interarrival time distribution, $F$, which is assumed to be IMRL (increasing mean residual life). It is shown that $E\phi(Z(t))$ is increasing in $t \geq 0$ for all increasing convex $\phi$. An example demonstrates that $Z(t)$ is not necessarily stochastically increasing nor is the renewal function necessarily concave. Both of these properties are known to hold for $F$ DFR (decreasing failure rate).

Citation

Download Citation

Mark Brown. "Further Monotonicity Properties for Specialized Renewal Processes." Ann. Probab. 9 (5) 891 - 895, October, 1981. https://doi.org/10.1214/aop/1176994317

Information

Published: October, 1981
First available in Project Euclid: 19 April 2007

zbMATH: 0489.60089
MathSciNet: MR628882
Digital Object Identifier: 10.1214/aop/1176994317

Subjects:
Primary: 60K05
Secondary: 60J25

Rights: Copyright © 1981 Institute of Mathematical Statistics

JOURNAL ARTICLE
5 PAGES


SHARE
Vol.9 • No. 5 • October, 1981
Back to Top