IDEAS home Printed from https://ideas.repec.org/a/spr/metrik/v87y2024i3d10.1007_s00184-023-00917-1.html
   My bibliography  Save this article

Ordering results for the smallest (largest) and the second smallest (second largest) order statistics of dependent and heterogeneous random variables

Author

Listed:
  • Omid Shojaee

    (University of Zabol)

  • Seyed Morteza Mohammadi

    (University of Zabol)

  • Reza Momeni

    (University of Zabol)

Abstract

In reliability theory, the kth order statistic represents the lifetime of a $$(n-k+1)$$ ( n - k + 1 ) -out-of-n system. In particular, the smallest (largest) order statistics denotes the lifetime of a series (parallel) system that consist of n components; and the second smallest (second largest) order statistics is the lifetime of a $$(n-1)$$ ( n - 1 ) -out-of-n (2-out-of-n) system. In this paper, sufficient conditions are provided to compare the smallest and the second smallest (largest and second largest) order statistics of dependent and heterogeneous random variables having the additive hazard model with the Archimedean copula in the sense of usual stochastic order and hazard rate order. Further, we compare the smallest order statistics of two sets of independent and heterogeneous random variables having the additive hazard model in the sense of dispersive order. Finally, our theoretical findings are evaluated by some numerical examples and counterexamples.

Suggested Citation

  • Omid Shojaee & Seyed Morteza Mohammadi & Reza Momeni, 2024. "Ordering results for the smallest (largest) and the second smallest (second largest) order statistics of dependent and heterogeneous random variables," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 87(3), pages 325-347, April.
    • Handle: RePEc:spr:metrik:v:87:y:2024:i:3:d:10.1007_s00184-023-00917-1
    DOI: 10.1007/s00184-023-00917-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00184-023-00917-1
    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/s00184-023-00917-1?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:metrik:v:87:y:2024:i:3:d:10.1007_s00184-023-00917-1. 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.