IDEAS home Printed from
   My bibliography  Save this article

Berry–Esseen and Edgeworth approximations for the normalized tail of an infinite sum of independent weighted gamma random variables


  • Veillette, Mark S.
  • Taqqu, Murad S.


Consider the sum Z=∑n=1∞λn(ηn−Eηn), where ηn are independent gamma random variables with shape parameters rn>0, and the λn’s are predetermined weights. We study the asymptotic behavior of the tail ∑n=M∞λn(ηn−Eηn), which is asymptotically normal under certain conditions. We derive a Berry–Esseen bound and Edgeworth expansions for its distribution function. We illustrate the effectiveness of these expansions on an infinite sum of weighted chi-squared distributions.

Suggested Citation

  • Veillette, Mark S. & Taqqu, Murad S., 2012. "Berry–Esseen and Edgeworth approximations for the normalized tail of an infinite sum of independent weighted gamma random variables," Stochastic Processes and their Applications, Elsevier, vol. 122(3), pages 885-909.
  • Handle: RePEc:eee:spapps:v:122:y:2012:i:3:p:885-909
    DOI: 10.1016/

    Download full text from publisher

    File URL:
    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.

    References listed on IDEAS

    1. Antonia Castaño-Martínez & Fernando López-Blázquez, 2005. "Distribution of a sum of weighted noncentral chi-square variables," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 14(2), pages 397-415, December.
    Full references (including those not matched with items on IDEAS)


    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:spapps:v:122:y:2012:i:3:p:885-909. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: .

    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.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.