Limiting distributions for a class of diminishing urn models

@inproceedings{Kuba2012LimitingDF,
  title={Limiting distributions for a class of diminishing urn models},
  author={Markus Kuba and Alois Panholzer},
  year={2012}
}
In this work we analyze a class of 2× 2 Pólya-Eggenberger urn models with ball replacement matrix M = (−a 0 c −d ) , a, d ∈ N, and c = p · a with p ∈ N0. We obtain limiting distributions for this 2 × 2 urn model 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… CONTINUE READING

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