IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v125y2017icp164-170.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715217300500
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2017.01.028?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. Pekalp, Mustafa Hilmi, 2022. "Some new bounds for the mean value function of the residual lifetime process," Statistics & Probability Letters, Elsevier, vol. 187(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chadjiconstantinidis, Stathis, 2023. "Some bounds for the renewal function and the variance of the renewal process," Applied Mathematics and Computation, Elsevier, vol. 436(C).
    2. Edita Kizinevič & Jonas Šiaulys, 2018. "The Exponential Estimate of the Ultimate Ruin Probability for the Non-Homogeneous Renewal Risk Model," Risks, MDPI, vol. 6(1), pages 1-17, March.
    3. Tautvydas Kuras & Jonas Sprindys & Jonas Šiaulys, 2020. "Martingale Approach to Derive Lundberg-Type Inequalities," Mathematics, MDPI, vol. 8(10), pages 1-18, October.
    4. Leipus, Remigijus & Siaulys, Jonas, 2007. "Asymptotic behaviour of the finite-time ruin probability under subexponential claim sizes," Insurance: Mathematics and Economics, Elsevier, vol. 40(3), pages 498-508, May.
    5. Remigijus Leipus & Jonas Šiaulys, 2009. "Asymptotic behaviour of the finite‐time ruin probability in renewal risk models," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(3), pages 309-321, May.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:125:y:2017:i:c:p:164-170. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.