IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v22y2020i4d10.1007_s11009-018-9681-9.html
   My bibliography  Save this article

Moments of the Forward Recurrence Time in a Renewal Process

Author

Listed:
  • Sotirios Losidis

    (University of Piraeus)

  • Konstadinos Politis

    (University of Piraeus)

Abstract

The forward recurrence time (also known as residual or excess lifetime) is one of the key quantities in renewal theory. The study of the variability of the forward recurrence time (as measured by the variance or the standard deviation) is important especially when we want to predict when the next event will occur. In this paper we study the moments of the forward recurrence time in a renewal process. In particular, we discuss the monotonicity of the variance for these recurrence times and study the covariance between the forward recurrence time at t and the number of renewals over [0,t]. The forward recurrence time practically applies in a number of cases. For example, in preventive replacement within any production process the forward recurrence time is the remaining time of the component. In medicine, for a chronic disease observed from one point onwards, the forward recurrence time is defined as the time in disease state until healing.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:22:y:2020:i:4:d:10.1007_s11009-018-9681-9
    DOI: 10.1007/s11009-018-9681-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-018-9681-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-018-9681-9?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. 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.
    2. Coleman, Rodney, 1982. "The moments of forward recurrence time," European Journal of Operational Research, Elsevier, vol. 9(2), pages 181-183, February.
    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. 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.
    2. 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.
    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. 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. Pekalp, Mustafa Hilmi, 2022. "Some new bounds for the mean value function of the residual lifetime process," Statistics & Probability Letters, Elsevier, vol. 187(C).
    6. 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.
    7. Dermitzakis, Vaios & Politis, Konstadinos, 2022. "Monotonicity properties for solutions of renewal equations," Statistics & Probability Letters, Elsevier, vol. 180(C).

    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:spr:metcap:v:22:y:2020:i:4:d:10.1007_s11009-018-9681-9. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.