Advanced Search
MyIDEAS: Login to save this article or follow this journal

Distributional analysis of a generalization of the Polya process


Author Info

  • Willmot, Gordon E.
Registered author(s):


    A nonhomogeneous birth process generalizing the Polya process is analyzed, and the distribution of the transition probabilities is shown to be the convolution of a negative binomial distribution and a compound Poisson distribution, whose secondary distribution is a mixture of zero-truncated geometric distributions. A simplified form of the secondary distribution is obtained when the transition intensities have a particular structure, and may sometimes be expressed in terms of Stirling numbers and special functions such as the incomplete gamma function, the incomplete beta function, and the exponential integral. Conditions under which the compound Poisson form of the marginal distributions may be improved to a geometric mixture are also given.

    Download Info

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
    File URL:
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

    Bibliographic Info

    Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

    Volume (Year): 47 (2010)
    Issue (Month): 3 (December)
    Pages: 423-427

    as in new window
    Handle: RePEc:eee:insuma:v:47:y:2010:i:3:p:423-427

    Contact details of provider:
    Web page:

    Related research

    Keywords: Nonhomogeneous birth process Negative binomial distribution Compound Poisson distribution Geometric distribution Completely monotone Mixture of geometrics Logarithmic series distribution STER distribution Incomplete gamma function Incomplete beta function Exponential integral Stirling numbers;


    No references listed on IDEAS
    You can help add them by filling out this form.



    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.


    Access and download statistics


    When requesting a correction, please mention this item's handle: RePEc:eee:insuma:v:47:y:2010:i:3:p:423-427. 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: (Zhang, Lei).

    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 references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link 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 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.