2009/02/05 by A. D. Barbour, Barbour, A. D. · 3 citations
Economics, Econometrics and Finance · Engineering · Mathematics · #Advanced Banach Space Theory #Applied mathematics #Approximations of π #Econometrics #Economic theories and models #Engineering #Fiscal Policy and Economic Growth #Mathematical analysis #Mathematics #Multivariate statistics #Occupancy #Physics #Scheme (mathematics) #Statistical physics #Statistics #Univariate #math.CO #math.PR #msc:60C05 #msc:60F05
paper · pdf · doi:10.48550/arxiv.0902.0879
published in arXiv (Cornell University) (Cornell University) · 20 pages
arxiv created 2009/02/05 · openalex publication_date 2009/02/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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).