IDEAS home Printed from https://ideas.repec.org/a/taf/japsta/v26y1999i3p355-371.html
   My bibliography  Save this article

Power transformation of the F distribution and a power normal family

Author

Listed:
  • Takafumi Isogai

Abstract

To transform the F distribution to a normal distribution, two types of formula for power transformation of the F variable are introduced. One formula is an extension of the Wilson-Hilferty transformation for the chi 2 variable, and the other type is based on the median of the F distribution. Combining those two formulas, a simple formula for the median of the F distribution is derived, and its numerical accuracy is evaluated. Simplification of the formula of the Wilson-Hilferty transformation, through the median formula, leads us to construct a power normal family from the generalized F distribution. Unlike the Box-Cox power normal family, our family has a property that the covariance structure of the maximum-likelihood estimates of the parameters is invariant under a scale transformation of the response variable. Numerical examples are given to show the diff erence between two power normal families.

Suggested Citation

  • Takafumi Isogai, 1999. "Power transformation of the F distribution and a power normal family," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(3), pages 355-371.
    • Handle: RePEc:taf:japsta:v:26:y:1999:i:3:p:355-371
    DOI: 10.1080/02664769922467
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/02664769922467
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/02664769922467?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.

    Citations

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


    Cited by:

    1. Takafumi Isogai & Hiroaki Uchida & Susumu Miyama & Sadao Nishiyama, 2008. "Statistical modeling of enamel rater value data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(5), pages 515-535.
    2. Takafumi Isogai, 2005. "Applications of a new power normal family," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(4), pages 421-436.

    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:26:y:1999:i:3:p:355-371. 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.