IDEAS home Printed from https://ideas.repec.org/a/ids/ijrsaf/v6y2012i4p311-337.html
   My bibliography  Save this article

Quantifying uncertainty in statistical distribution of small sample data using Bayesian inference of unbounded Johnson distribution

Author

Listed:
  • Kun Marhadi
  • Satchi Venkataraman
  • Shantaram S. Pai

Abstract

Probabilistic analysis of physical systems requires information on the distributions of random variables. Distributions are typically obtained from testing or field data. In engineering design where tests are expensive, the sample size of such data is small O(10). Identifying correct distributions with small number of samples is difficult. Furthermore, parameters of assumed distributions obtained from small sample data themselves contain some uncertainty. In this study a Johnson SU family distribution function is used to identify shape, location and scale parameters of distribution that can best fit small sample data. A Bayesian inference procedure is used to determine distributions of the parameters. We show that the procedure correctly bounds the tail regions of the distributions and is less conservative than bounds obtained using bootstrap methods.

Suggested Citation

  • Kun Marhadi & Satchi Venkataraman & Shantaram S. Pai, 2012. "Quantifying uncertainty in statistical distribution of small sample data using Bayesian inference of unbounded Johnson distribution," International Journal of Reliability and Safety, Inderscience Enterprises Ltd, vol. 6(4), pages 311-337.
    • Handle: RePEc:ids:ijrsaf:v:6:y:2012:i:4:p:311-337
    as

    Download full text from publisher

    File URL: http://www.inderscience.com/link.php?id=49596
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

    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:ids:ijrsaf:v:6:y:2012:i:4:p:311-337. 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: Sarah Parker (email available below). General contact details of provider: http://www.inderscience.com/browse/index.php?journalID=98 .

    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.