March 2012 Limiting distributions for a class of diminishing urn models
Markus Kuba, Alois Panholzer
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Adv. in Appl. Probab. 44(1): 87-116 (March 2012). DOI: 10.1239/aap/1331216646


In this work we analyze a class of 2 x 2 Pólya-Eggenberger urn models with ball replacement matrix M = (-a 0 \\ c -d), a, dN and c = pa with pN0. We determine limiting distributions by obtaining a precise recursive description of the moments of the considered random variables, which allows us to deduce asymptotic expansions of the moments. In particular, we obtain limiting distributions for the pills problem a = c = d = 1, originally proposed by Knuth and McCarthy. Furthermore, we also obtain limiting distributions for the well-known sampling without replacement urn, a = d = 1 and c = 0, and generalizations of it to arbitrary a, dN and c = 0. Moreover, we obtain a recursive description of the moment sequence for a generalized problem.


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Markus Kuba. Alois Panholzer. "Limiting distributions for a class of diminishing urn models." Adv. in Appl. Probab. 44 (1) 87 - 116, March 2012.


Published: March 2012
First available in Project Euclid: 8 March 2012

zbMATH: 1300.60023
MathSciNet: MR2951548
Digital Object Identifier: 10.1239/aap/1331216646

Primary: 60C05

Keywords: diminishing urn , pills problem , Pólya-Eggenberger urn model , sampling without replacement

Rights: Copyright © 2012 Applied Probability Trust


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Vol.44 • No. 1 • March 2012
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