Geodesic
Mixed Negative Binomial Distribution by Weighted Gamma Mixing Distribution
Mathematics and Education in Mathematics, Tome 40 (2011) no. 1, pp. 327-331.

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In this paper the mixed negative binomial distribution, known also as P´olya distribution is considered. We suppose that the mixing distribution is a weighted Gamma distribution. We derive the probability mass function and consider some special cases. The Panjer recursion formulas and some properties are given.
Keywords: Binomial Distribution, Gamma Distribution 
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     author = {Stoynov, Pavel},
     title = {Mixed {Negative} {Binomial} {Distribution} by {Weighted} {Gamma} {Mixing} {Distribution}},
     journal = {Mathematics and Education in Mathematics},
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Stoynov, Pavel. Mixed Negative Binomial Distribution by Weighted Gamma Mixing Distribution. Mathematics and Education in Mathematics, Tome 40 (2011) no. 1, pp. 327-331. http://geodesic.mathdoc.fr/item/MEM_2011_40_1_a38/