 Distributional analysis of a generalization of the Polya processGordon E. Willmot Insurance: Mathematics and Economics, 2010, vol. 47, issue 3, 423-427 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. 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 (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:47:y:2010:i:3:p:423-427 Access Statistics for this article Insurance: Mathematics and Economics is currently edited by R. Kaas, Hansjoerg Albrecher, M. J. Goovaerts and E. S. W. Shiu More articles in Insurance: Mathematics and Economics from Elsevier |
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