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A two-sided bound for the renewal function when the interarrival distribution is IMRL

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  • Losidis, Sotirios
  • Politis, Konstadinos

Abstract

We obtain an upper and a lower bound for the renewal function in a renewal process with IMRL lifetimes. The lower bound improves a well-known bound by Brown (1980). We study the performance of these bounds both theoretically and with the aid of numerical examples.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:125:y:2017:i:c:p:164-170
    DOI: 10.1016/j.spl.2017.01.028
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    References listed on IDEAS

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    1. Geluk, J.L. & Frenk, J.B.G., 2011. "Renewal theory for random variables with a heavy tailed distribution and finite variance," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 77-82, January.
    2. Sgibnev, M. S., 1997. "Submultiplicative moments of the supremum of a random walk with negative drift," Statistics & Probability Letters, Elsevier, vol. 32(4), pages 377-383, April.
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    Citations

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    Cited by:

    1. 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.
    2. Landy Rabehasaina & Jae-Kyung Woo, 2018. "On a multivariate renewal-reward process involving time delays and discounting: applications to IBNR processes and infinite server queues," Queueing Systems: Theory and Applications, Springer, vol. 90(3), pages 307-350, December.
    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.
    4. Sotirios Losidis & Konstadinos Politis, 2020. "Moments of the Forward Recurrence Time in a Renewal Process," Methodology and Computing in Applied Probability, Springer, vol. 22(4), pages 1591-1600, December.
    5. Chadjiconstantinidis, Stathis, 2023. "Some bounds for the renewal function and the variance of the renewal process," Applied Mathematics and Computation, Elsevier, vol. 436(C).
    6. Sotirios Losidis & Konstadinos Politis & Georgios Psarrakos, 2021. "Exact Results and Bounds for the Joint Tail and Moments of the Recurrence Times in a Renewal Process," Methodology and Computing in Applied Probability, Springer, vol. 23(4), pages 1489-1505, December.
    7. Dermitzakis, Vaios & Politis, Konstadinos, 2022. "Monotonicity properties for solutions of renewal equations," Statistics & Probability Letters, Elsevier, vol. 180(C).
    8. 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.
    9. Pekalp, Mustafa Hilmi, 2022. "Some new bounds for the mean value function of the residual lifetime process," Statistics & Probability Letters, Elsevier, vol. 187(C).

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