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Intuitive approximations for the renewal function

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  • Mitov, Kosto V.
  • Omey, Edward

Abstract

It is hard to find explicit expressions for the renewal function U(x)=∑n=0∞F∗n(x). Many researchers have made attempts to find suitable approximations for U(x). In this paper we present simple approximations and show that they cover many of the known results.

Suggested Citation

  • Mitov, Kosto V. & Omey, Edward, 2014. "Intuitive approximations for the renewal function," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 72-80.
    • Handle: RePEc:eee:stapro:v:84:y:2014:i:c:p:72-80
    DOI: 10.1016/j.spl.2013.09.030
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    References listed on IDEAS

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    1. Ney, Peter, 1981. "A refinement of the coupling method in renewal theory," Stochastic Processes and their Applications, Elsevier, vol. 11(1), pages 11-26, March.
    2. Omey, E. & Willekens, E., 1986. "Second order behaviour of the tail of a subordinated probability distribution," Stochastic Processes and their Applications, Elsevier, vol. 21(2), pages 339-353, February.
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    Cited by:

    1. Slavtchova-Bojkova, Maroussia & Trayanov, Plamen & Dimitrov, Stoyan, 2017. "Branching processes in continuous time as models of mutations: Computational approaches and algorithms," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 111-124.
    2. Omey, Edward & Van Gulck, Stefan, 2015. "Intuitive approximations in discrete renewal theory, Part 1: Regularly varying case," Statistics & Probability Letters, Elsevier, vol. 104(C), pages 68-74.
    3. Dermitzakis, Vaios & Politis, Konstadinos, 2022. "Monotonicity properties for solutions of renewal equations," Statistics & Probability Letters, Elsevier, vol. 180(C).

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