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  • Cited by 2
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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Kim, Yunbae and Hwang, Ganguk 2015. Design and Analysis of Medium Access Protocol: Throughput and Short-Term Fairness Perspective. IEEE/ACM Transactions on Networking, Vol. 23, Issue. 3, p. 959.

    Liu, Nan 2011. Wiley Encyclopedia of Operations Research and Management Science.

  • Probability in the Engineering and Informational Sciences, Volume 20, Issue 2
  • April 2006, pp. 231-250


  • Konstadinos Politis (a1) and Markos V. Koutras (a1)
  • DOI:
  • Published online: 01 April 2006

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.

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Probability in the Engineering and Informational Sciences
  • ISSN: 0269-9648
  • EISSN: 1469-8951
  • URL: /core/journals/probability-in-the-engineering-and-informational-sciences
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