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Distributional analysis of a generalization of the Polya process

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  • Willmot, Gordon E.
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    Abstract

    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.

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    Bibliographic Info

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

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

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    Handle: RePEc:eee:insuma:v:47:y:2010:i:3:p:423-427

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    Web page: http://www.elsevier.com/locate/inca/505554

    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;

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