Univariate approximations in the infinite occupancy scheme

Details Univariate approximations in the infinite occupancy scheme Univariate approximations in the infinite occupancy scheme

2009-02-05

arxiv.org/abs/0902.0879v1

Mathematics

Probability

20 pages

Scientific paper

The paper concerns the classical occupancy scheme with infinitely many boxes. We establish approximations to the distributions of the number of occupied boxes, and of the number of boxes containing exactly r balls, within the family of translated Poisson distributions. These are shown to be of ideal asymptotic order, with respect both to total variation distance and to the approximation of point probabilities. The proof is probabilistic, making use of a translated Poisson approximation theorem of R\"ollin (2005).

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