Open Access
August, 1984 Normal Approximations to Sums of Scores Based on Occupancy Numbers
M. P. Quine, J. Robinson
Ann. Probab. 12(3): 794-804 (August, 1984). DOI: 10.1214/aop/1176993228


A central limit theorem and remainder term estimates are given for the distribution of the sum of scores based on the occupancy numbers resulting from the random allocation of $N$ balls to $n$ boxes. The proof involves bivariate characteristic functions, exploiting the equivalence of multinomial and conditioned Poisson variables. The results are shown to include the statistics for the empty cell test, the chi-squared test and the likelihood ratio test.


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M. P. Quine. J. Robinson. "Normal Approximations to Sums of Scores Based on Occupancy Numbers." Ann. Probab. 12 (3) 794 - 804, August, 1984.


Published: August, 1984
First available in Project Euclid: 19 April 2007

zbMATH: 0584.60031
MathSciNet: MR744234
Digital Object Identifier: 10.1214/aop/1176993228

Primary: 60F05

Keywords: Berry-Esseen bound , central limit theorem , multinomial sums , occupancy schemes

Rights: Copyright © 1984 Institute of Mathematical Statistics

Vol.12 • No. 3 • August, 1984
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