Author:
Politis Konstadinos,Koutras Markos V.
Abstract
In the literature, most of the bounds for the renewal function
U(x) corresponding to a lifetime distribution F
are given in terms of the first two moments of F only. The best
general upper bound of this type is the one given in Lorden (1970). In the
present article, we show that improved bounds can be obtained if one
exploits the specific form of the distribution F. We derive a
bound that improves upon Lorden's, at least on an interval
[0,a) with a ≤ ∞, and we give both
sufficient and necessary conditions for this improvement to hold uniformly
for x ≥ 0. Refined upper as well as lower bounds are given for
the case where F belongs to a class of distributions with
monotone aging or when the renewal density is monotone.
Publisher
Cambridge University Press (CUP)
Subject
Industrial and Manufacturing Engineering,Management Science and Operations Research,Statistics, Probability and Uncertainty,Statistics and Probability
Cited by
16 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献