IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v80y2010i23-24p1870-1874.html
   My bibliography  Save this article

The limiting behavior of some infinitely divisible exponential dispersion models

Author

Listed:
  • Bar-Lev, Shaul K.
  • Letac, Gérard

Abstract

Consider an exponential dispersion model (EDM) generated by a probability [mu] on [0,[infinity]) which is infinitely divisible with an unbounded Lévy measure [nu]. The Jørgensen set (i.e., the dispersion parameter space) is then , in which case the EDM is characterized by two parameters: [theta]0, the natural parameter of the associated natural exponential family, and the Jørgensen (or dispersion) parameter, t. Denote the corresponding distribution by and let Yt be a r.v. with distribution . Then for [nu]((x,[infinity]))~-llogx around zero, we prove that the limiting law F0 of as t-->0 is a Pareto type law (not depending on [theta]0) with the form F0(u)=0 for u =1. This result enables an approximation of the distribution of Yt to be found for relatively small values of the dispersion parameter of the corresponding EDM. Illustrative examples are provided.

Suggested Citation

  • Bar-Lev, Shaul K. & Letac, Gérard, 2010. "The limiting behavior of some infinitely divisible exponential dispersion models," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1870-1874, December.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:23-24:p:1870-1874
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(10)00236-1
    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

    as
    1. Bar-Lev, Shaul K. & Enis, Peter, 1987. "Existence of moments and an asymptotic result based on a mixture of exponential distributions," Statistics & Probability Letters, Elsevier, vol. 5(4), pages 273-277, June.
    2. Kokonendji, Célestin C. & Khoudar, Mohamed, 2006. "On Lévy measures for infinitely divisible natural exponential families," Statistics & Probability Letters, Elsevier, vol. 76(13), pages 1364-1368, July.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Bar-Lev, Shaul K. & Kella, Offer & Löpker, Andreas, 2013. "Small parameter behavior of families of distributions," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 783-789.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bar-Lev, Shaul K. & Kella, Offer & Löpker, Andreas, 2013. "Small parameter behavior of families of distributions," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 783-789.
    2. Kella, Offer & Löpker, Andreas, 2013. "Weak convergence of subordinators to extremal processes," Stochastic Processes and their Applications, Elsevier, vol. 123(8), pages 3122-3131.
    3. Yacouba Boubacar Maïnassara & Célestin Kokonendji, 2014. "On normal stable Tweedie models and power-generalized variance functions of only one component," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(3), pages 585-606, September.
    4. Louati, Mahdi & Masmoudi, Afif, 2015. "Moment for the inverse Riesz distributions," Statistics & Probability Letters, Elsevier, vol. 102(C), pages 30-37.
    5. Vinogradov, Vladimir, 2011. "On Kendall-Ressel and related distributions," Statistics & Probability Letters, Elsevier, vol. 81(10), pages 1493-1501, October.

    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:80:y:2010:i:23-24:p:1870-1874. 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.

    If CitEc recognized a bibliographic 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.

    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.