IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v65y2024i3d10.1007_s00362-023-01413-4.html
   My bibliography  Save this article

On approximation and estimation of distribution function of sum of independent random variables

Author

Listed:
  • N. N. Midhu

    (IQVIA)

  • Isha Dewan

    (Indian Statistical Institute)

  • K. K. Sudheesh

    (Indian Statistical Institute)

  • E. P. Sreedevi

    (Maharaja’s College)

Abstract

In this paper, we obtain an approximation for the distribution function of sum of two independent random variables using quantile based representation. The error of approximation is shown to be negligible under some mild conditions. We then use the approximation to obtain a non-parametric estimator for the distribution function of sum of two independent random variables. The exact distribution of the proposed estimator is derived. The estimator is shown to be strongly consistent and asymptotically normally distributed. Extensive Monte Carlo simulation studies are carried out to evaluate the bias and mean squared error of the estimator and also to assess the approximation error. We also compare the performance of the proposed estimator with other estimators available in the literature. Finally, we illustrate the use of the proposed estimator for estimating the reliability function of a standby redundant system.

Suggested Citation

  • N. N. Midhu & Isha Dewan & K. K. Sudheesh & E. P. Sreedevi, 2024. "On approximation and estimation of distribution function of sum of independent random variables," Statistical Papers, Springer, vol. 65(3), pages 1437-1467, May.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:3:d:10.1007_s00362-023-01413-4
    DOI: 10.1007/s00362-023-01413-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-023-01413-4
    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/s00362-023-01413-4?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.

    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:stpapr:v:65:y:2024:i:3:d:10.1007_s00362-023-01413-4. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.