The Annals of Probability

Further Monotonicity Properties for Specialized Renewal Processes

Mark Brown

Full-text: Open access

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).

Article information

Source
Ann. Probab. Volume 9, Number 5 (1981), 891-895.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aop/1176994317

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/aop/1176994317

Mathematical Reviews number (MathSciNet)
MR628882

Zentralblatt MATH identifier
0489.60089

Subjects
Primary: 60K05: Renewal theory
Secondary: 60J25: Continuous-time Markov processes on general state spaces

Keywords
Renewal theory IMRL and DFR distributions monotonicity properties for stochastic processes forward and backward recurrence times

Citation

Brown, Mark. Further Monotonicity Properties for Specialized Renewal Processes. The Annals of Probability 9 (1981), no. 5, 891--895. doi:10.1214/aop/1176994317. http://projecteuclid.org/euclid.aop/1176994317.


Export citation