IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v79y2009i14p1621-1629.html
   My bibliography  Save this article

Variance stabilizing transformations of Poisson, binomial and negative binomial distributions

Author

Listed:
  • Yu, Guan

Abstract

Consider variance stabilizing transformations of Poisson distribution [pi]([lambda]), binomial distribution B(n,p) and negative binomial distribution NB(r,p), with square root transformations for [pi]([lambda]), arcsin transformations for B(n,p) and inverse hyperbolic sine transformations for NB(r,p). We will introduce three terms: critical point, domain of dependence and relative error. By comparing the relative errors of the transformed variances of [pi]([lambda]), B(n,p) and NB(r,p), and comparing the skewness and kurtosis of [pi]([lambda]), B(n,p) and NB(r,p) and their transformed variables, we obtain some better transformations with domains of dependence of the parameters. A new kind of transformation for B(n,p) is suggested.

Suggested Citation

  • Yu, Guan, 2009. "Variance stabilizing transformations of Poisson, binomial and negative binomial distributions," Statistics & Probability Letters, Elsevier, vol. 79(14), pages 1621-1629, July.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:14:p:1621-1629
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(09)00147-3
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Malay Ghosh & Tamal Ghosh & Masayo Y. Hirose, 2022. "Poisson Counts, Square Root Transformation and Small Area Estimation," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 449-471, November.

    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:eee:stapro:v:79:y:2009:i:14:p:1621-1629. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.