IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v187y2022ics0167715222000803.html
   My bibliography  Save this article

Some new bounds for the mean value function of the residual lifetime process

Author

Listed:
  • Pekalp, Mustafa Hilmi

Abstract

In this study, mean residual lifetime (MRL) function of the residual lifetime process is investigated. Various two-sided bounds are obtained for this function by using the monotone convergence of the sequence of the functions. Since many important features of any stochastic process depend on classifications of distributions, improved bounds are found for MRL function by considering the taxonomy of the distributions. Moreover, some new bounds are achieved by using the asymptotic expression of MRL function and its boundary relation with the MRL of a single component at age t. Three examples are given to illustrate the results proposed.

Suggested Citation

  • Pekalp, Mustafa Hilmi, 2022. "Some new bounds for the mean value function of the residual lifetime process," Statistics & Probability Letters, Elsevier, vol. 187(C).
  • Handle: RePEc:eee:stapro:v:187:y:2022:i:c:s0167715222000803
    DOI: 10.1016/j.spl.2022.109497
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715222000803
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.spl.2022.109497?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. Politis, Konstadinos, 2005. "Bounds for the probability and severity of ruin in the Sparre Andersen model," Insurance: Mathematics and Economics, Elsevier, vol. 36(2), pages 165-177, April.
    2. 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.
    3. Manuel P. Baganha & Geraldo Ferrer & David F. Pyke, 1999. "The residual life of the renewal process: A simple algorithm," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(4), pages 435-443, June.
    4. 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.
    Full references (including those not matched with items on IDEAS)

    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. Psarrakos, Georgios & Politis, Konstadinos, 2008. "Tail bounds for the joint distribution of the surplus prior to and at ruin," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 163-176, February.
    2. Chadjiconstantinidis, Stathis & Xenos, Panos, 2022. "Refinements of bounds for tails of compound distributions and ruin probabilities," Applied Mathematics and Computation, Elsevier, vol. 421(C).
    3. 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.
    4. Chadjiconstantinidis, Stathis, 2023. "Some bounds for the renewal function and the variance of the renewal process," Applied Mathematics and Computation, Elsevier, vol. 436(C).
    5. 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.
    6. Lee, David & Li, Wai Keung & Wong, Tony Siu Tung, 2012. "Modeling insurance claims via a mixture exponential model combined with peaks-over-threshold approach," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 538-550.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. Woo, Jae-Kyung, 2011. "Refinements of two-sided bounds for renewal equations," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 189-196, March.
    12. Psarrakos, Georgios, 2009. "A note on convolutions of compound geometric distributions," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1231-1237, May.
    13. Stathis Chadjiconsatntinidis, 2024. "Two-sided Bounds for Renewal Equations and Ruin Quantities," Methodology and Computing in Applied Probability, Springer, vol. 26(2), pages 1-54, June.
    14. Eugenia Babiloni & Ester Guijarro & Juan R. Trapero, 2023. "Stock control analytics: a data-driven approach to compute the fill rate considering undershoots," Operational Research, Springer, vol. 23(1), pages 1-25, March.
    15. 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.
    16. Dermitzakis, Vaios & Politis, Konstadinos, 2022. "Monotonicity properties for solutions of renewal equations," Statistics & Probability Letters, Elsevier, vol. 180(C).
    17. Psarrakos, Georgios, 2008. "Tail bounds for the distribution of the deficit in the renewal risk model," Insurance: Mathematics and Economics, Elsevier, vol. 43(2), pages 197-202, October.

    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:187:y:2022:i:c:s0167715222000803. 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.