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.
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 $M= \binom{ -a \,0}{c -d}, a,d∈\mathbb{N}$ and $c∈\mathbb{N} _0$. 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, $a,d∈\mathbb{N}$ and $c=0$.
Kuba, Markus; Panholzer, Alois, 2010, On The Area Under Lattice Paths Associated With Triangular Diminishing Urn Models, Advances In Applied Mathematics, 44, 4, pp. 329-358, 10.1016/j.aam.2009.09.001.
Kuba, Markus; Panholzer, Alois, 2011, Analysis Of Statistics For Generalized Stirling Permutations, Combinatorics, Probability And Computing, 20, 6, pp. 875-910, 10.1017/s0963548311000381.