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August, 1981 A Remainder Term Estimate for the Normal Approximation in Classical Occupancy
Gunnar Englund
Ann. Probab. 9(4): 684-692 (August, 1981). DOI: 10.1214/aop/1176994376

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 $Z_n$ be the number of occupied boxes (i.e., boxes containing at least one ball) after $n$ throws. It is well known that $Z_n$ 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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Gunnar Englund. "A Remainder Term Estimate for the Normal Approximation in Classical Occupancy." Ann. Probab. 9 (4) 684 - 692, August, 1981. https://doi.org/10.1214/aop/1176994376

Information

Published: August, 1981
First available in Project Euclid: 19 April 2007

zbMATH: 0464.60025
MathSciNet: MR624696
Digital Object Identifier: 10.1214/aop/1176994376

Subjects:
Primary: 60F05

Keywords: Classical occupancy , Normal approximation , remainder term

Rights: Copyright © 1981 Institute of Mathematical Statistics

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Vol.9 • No. 4 • August, 1981
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