Markus Kuba ; Alois Panholzer
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Limit laws for a class of diminishing urn models.
dmtcs:3519 -
Discrete Mathematics & Theoretical Computer Science,
January 1, 2007,
DMTCS Proceedings vol. AH, 2007 Conference on Analysis of Algorithms (AofA 07)
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https://doi.org/10.46298/dmtcs.3519
Limit laws for a class of diminishing urn models.Conference paper
Authors: Markus Kuba 1; Alois Panholzer 1
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Markus Kuba;Alois Panholzer
1 Institut für Diskrete Mathematik und Geometrie [Wien]
In this work we analyze a class of diminishing 2×2 Pólya-Eggenberger urn models with ball replacement matrix M given by M=(−a0c−d),a,d∈N and c∈N0. We obtain limit laws for this class of 2×2 urns by giving estimates for the moments of the considered random variables. As a special instance we obtain limit laws for the pills problem, proposed by Knuth and McCarthy, which corresponds to the special case a=c=d=1. Furthermore, we also obtain limit laws for the well known sampling without replacement urn, a=d=1 and c=0, and corresponding generalizations, a,d∈N and c=0.