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).
Publié le : 1981-10-14
Classification:
Renewal theory,
IMRL and DFR distributions,
monotonicity properties for stochastic processes,
forward and backward recurrence times,
60K05,
60J25
@article{1176994317,
author = {Brown, Mark},
title = {Further Monotonicity Properties for Specialized Renewal Processes},
journal = {Ann. Probab.},
volume = {9},
number = {6},
year = {1981},
pages = { 891-895},
language = {en},
url = {http://dml.mathdoc.fr/item/1176994317}
}
Brown, Mark. Further Monotonicity Properties for Specialized Renewal Processes. Ann. Probab., Tome 9 (1981) no. 6, pp. 891-895. http://gdmltest.u-ga.fr/item/1176994317/