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Bounds for the Renewal Function and Related Quantities

Author

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  • Sotirios Losidis

    (University of Piraeus)

  • Konstadinos Politis

    (University of Piraeus)

Abstract

We obtain new bounds for the renewal function, as well as for the expected number of renewals over an interval $$(t,t+h]$$ ( t , t + h ] . Improved bounds are given when the interarrival distribution belongs to certain aging classes. Our results are compared with existing ones in the literature, both theoretically and with the aid of numerical resuts.

Suggested Citation

  • Sotirios Losidis & Konstadinos Politis, 2022. "Bounds for the Renewal Function and Related Quantities," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2647-2660, December.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:4:d:10.1007_s11009-022-09953-2
    DOI: 10.1007/s11009-022-09953-2
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    References listed on IDEAS

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    1. Chadjiconstantinidis, Stathis & Politis, Konstadinos, 2007. "Two-sided bounds for the distribution of the deficit at ruin in the renewal risk model," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 41-52, July.
    2. Woo, Jae-Kyung, 2011. "Refinements of two-sided bounds for renewal equations," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 189-196, March.
    3. Losidis, Sotirios & Politis, Konstadinos, 2017. "A two-sided bound for the renewal function when the interarrival distribution is IMRL," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 164-170.
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    Citations

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    Cited by:

    1. Asadi, Majid, 2023. "On a parametric model for the mean number of system repairs with applications," Reliability Engineering and System Safety, Elsevier, vol. 234(C).
    2. Stathis Chadjiconstantinidis, 2024. "Two-sided Bounds for some Quantities in the Delayed Renewal Process," Methodology and Computing in Applied Probability, Springer, vol. 26(3), pages 1-48, September.
    3. Stathis Chadjiconstantinidis, 2023. "Sequences of Improved Two-Sided Bounds for the Renewal Function and the Solutions of Renewal-Type Equations," Methodology and Computing in Applied Probability, Springer, vol. 25(2), pages 1-31, June.

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