Univariate approximations in the infinite occupancy scheme
نویسنده
چکیده
In the classical occupancy scheme with infinitely many boxes, n balls are thrown independently into boxes 1, 2, . . ., with probabilities pj , j ≥ 1. We establish approximations to the distributions of the summary statistics Kn, the number of occupied boxes, and Kn,r, the number of boxes containing exactly r balls, within the family of translated Poisson distributions. These are shown to be of ideal order as n → ∞, 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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