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A Remainder Term Estimate for the Normal Approximation in Classical Occupancy

Gunnar Englund
The Annals of Probability
Vol. 9, No. 4 (Aug., 1981), pp. 684-692
Stable URL: http://www.jstor.org/stable/2243423
Page Count: 9
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
A Remainder Term Estimate for the Normal Approximation in Classical Occupancy
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Abstract

Let balls be thrown successively at random into N boxes, such that each ball falls into any box with the same probability 1/N. Let Zn be the number of occupied boxes (i.e., boxes containing at least one ball) after n throws. It is well known that Zn is approximately normally distributed under general conditions. We give a remainder term estimate, which is of the correct order of magnitude. In fact we prove that $0.087/\max(3, DZ_n) \leqq \sup_x |P(Z_n < x) - \Phi((x - EZ_n)/DZ_n)| \leqq 10.4/DZ_n.$

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