Permanent URL to this publication: http://dx.doi.org/10.5167/uzh21237
Barbour, A D; Gnedin, A (2009). Small counts in the infinite occupancy scheme. Electronic Journal of Probability, 14(13):365384.

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Abstract
The paper is concerned with the classical occupancy scheme in which balls are thrown independently into infinitely many boxes, with given probability of hitting each of the boxes. We establish joint normal approximation, as the number of balls goes to infinity, for the numbers of boxes containing any fixed number of balls, standardized in the natural way, assuming only that the variances of these counts all tend to infinity. The proof of this approximation is based on a dePoissonization lemma. We then review sufficient conditions for the variances to tend to infinity. Typically, the normal approximation does not mean convergence. We show that the convergence of the full vector of counts only holds under a condition of regular variation, thus giving a complete characterization of possible limit correlation structures.
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Additional indexing
Item Type:  Journal Article, refereed, original work 

Communities & Collections:  07 Faculty of Science > Institute of Mathematics 
DDC:  510 Mathematics 
Language:  English 
Date:  9 February 2009 
Deposited On:  16 Nov 2009 20:25 
Last Modified:  27 Nov 2013 20:35 
Publisher:  Institute of Mathematical Statistics 
ISSN:  10836489 
Official URL:  http://www.emis.de/journals/EJPECP/_ejpecp/viewarticle77b2.html?id=1912 
Related URLs:  http://arxiv.org/abs/0809.4387 http://www.math.washington.edu/~ejpecp/ 
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