IDEAS home Printed from https://ideas.repec.org/a/taf/japsta/v47y2020i13-15p2749-2764.html
   My bibliography  Save this article

Computing the exact distribution of the Bartlett's test statistic by numerical inversion of its characteristic function

Author

Listed:
  • Viktor Witkovský

Abstract

Application of the exact statistical inference frequently leads to non-standard probability distributions of the considered estimators or test statistics. The exact distributions of many estimators and test statistics can be specified by their characteristic functions, as is the case for the null distribution of the Bartlett's test statistic. However, analytical inversion of the characteristic function, if possible, frequently leads to complicated expressions for computing the distribution function and the corresponding quantiles. An efficient alternative is the well-known method based on numerical inversion of the characteristic functions, which is, however, ignored in popular statistical software packages. In this paper, we present the explicit characteristic function of the corrected Bartlett's test statistic together with the computationally fast and efficient implementation of the approach based on numerical inversion of this characteristic function, suggested for evaluating the exact null distribution used for testing homogeneity of variances in several normal populations, with possibly unequal sample sizes.

Suggested Citation

  • Viktor Witkovský, 2020. "Computing the exact distribution of the Bartlett's test statistic by numerical inversion of its characteristic function," Journal of Applied Statistics, Taylor & Francis Journals, vol. 47(13-15), pages 2749-2764, November.
    • Handle: RePEc:taf:japsta:v:47:y:2020:i:13-15:p:2749-2764
    DOI: 10.1080/02664763.2019.1675608
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/02664763.2019.1675608
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/02664763.2019.1675608?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.

    More about this item

    Statistics

    Access and download statistics

    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:taf:japsta:v:47:y:2020:i:13-15:p:2749-2764. 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 Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/CJAS20 .

    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.