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# Limit laws for a class of diminishing urn models.

Abstract : 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 $c=0$.
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https://hal.inria.fr/hal-01184767
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Submitted on : Monday, August 17, 2015 - 4:58:42 PM
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dmAH0126.pdf
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• HAL Id : hal-01184767, version 1

### Citation

Markus Kuba, Alois Panholzer. Limit laws for a class of diminishing urn models.. 2007 Conference on Analysis of Algorithms, AofA 07, 2007, Juan les Pins, France. pp.377-388. ⟨hal-01184767⟩

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