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Univariate approximations in the infinite occupancy scheme


Barbour, A D (2009). Univariate approximations in the infinite occupancy scheme. ALEA Latin American Journal of Probability and Mathematical Statistics, 6:415-433.

Abstract

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).

Abstract

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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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2009
Deposited On:28 Jan 2010 09:58
Last Modified:26 Jan 2017 08:46
Publisher:Instituto Nacional de Matematica Pura e Aplicada (IMPA), Brazil
ISSN:1980-0436
Official URL:http://alea.impa.br/portugues/index_v6.htm
Related URLs:http://arxiv.org/abs/0902.0879v1

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