Univariate approximations in the infinite occupancy scheme

2009/02/05 by A. D. Barbour, Barbour, A. D.
Economics, Econometrics and Finance · Mathematics · #Economic theories and models #Fiscal Policy and Economic Growth #Advanced Banach Space Theory

paper · pdf · doi:10.48550/arxiv.0902.0879

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 Röllin (2005).

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