IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v32y1984i4p917-925.html
   My bibliography  Save this article

Extensions of the Freund Distribution with Applications in Reliability Theory

Author

Listed:
  • Moshe Shaked

    (University of Arizona, Tucson, Arizona)

Abstract

The Freund distribution models situations in which the exponential residual lifetime of one component depends on the working status of another component. The literature has discussed generalizations and analogs of the Freund distribution. Such generalizations can be obtained by replacing exponential random variables by Weibull or gamma random variables, or by compounding (mixing) Freund distributions. This paper shows how to unify various well-known generalizations of the Freund distribution by using one simple functional representation. This functional representation has a physical meaning that sheds new light on the meaning of some of these generalizations. Furthermore, using this functional representation, we derive various properties of the Freund distribution and its extensions. In particular, we show that some random variables, which have the Freund distribution or one of its extensions, are positively associated and also belong to some classes of multivariate “increasing failure rate average” and “new better than used” distributions. These properties provide bounds for various probabilistic quantities of interest in reliability theory.

Suggested Citation

  • Moshe Shaked, 1984. "Extensions of the Freund Distribution with Applications in Reliability Theory," Operations Research, INFORMS, vol. 32(4), pages 917-925, August.
    • Handle: RePEc:inm:oropre:v:32:y:1984:i:4:p:917-925
    DOI: 10.1287/opre.32.4.917
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.32.4.917
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.32.4.917?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
    ---><---

    Citations

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


    Cited by:

    1. Li, Haijun, 2003. "Association of multivariate phase-type distributions, with applications to shock models," Statistics & Probability Letters, Elsevier, vol. 64(4), pages 381-392, October.
    2. Hyunju Lee & Ji Hwan Cha, 2020. "A new general class of discrete bivariate distributions constructed by using the likelihood ratio," Statistical Papers, Springer, vol. 61(3), pages 923-944, June.
    3. Franco, Manuel & Vivo, Juana-Maria & Kundu, Debasis, 2020. "A generalized Freund bivariate model for a two-component load sharing system," Reliability Engineering and System Safety, Elsevier, vol. 203(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:inm:oropre:v:32:y:1984:i:4:p:917-925. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.