IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-1-4612-3990-1_6.html
   My bibliography  Save this book chapter

On a Class of Symmetric Nonnormal Distributions with a Kurtosis of Three

In: Statistical Theory and Applications

Author

Listed:
  • B. K. Kale
  • G. Sebastian

Abstract

It is well known that within the Pearsonian system the normal distribution is uniquely determined by the condition that skewness is zero and kurtosis is 3. We construct a wide class of non-normal symmetric distributions with kurtosis equal to 3. The distributions presented here can be used in linear models as an alternative to the normal error. However, many distributions in this class can be very much different from the normal distribution in the tail as well as the central part of the distribution. Further, any test of normality based on sample skewness and/or sample kurtosis would have power zero against these alternatives.

Suggested Citation

  • B. K. Kale & G. Sebastian, 1996. "On a Class of Symmetric Nonnormal Distributions with a Kurtosis of Three," Springer Books, in: H. N. Nagaraja & Pranab Kumar Sen & Donald F. Morrison (ed.), Statistical Theory and Applications, chapter 6, pages 55-63, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-3990-1_6
    DOI: 10.1007/978-1-4612-3990-1_6
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    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:spr:sprchp:978-1-4612-3990-1_6. 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.