The Annals of Probability

Normal Approximations to Sums of Scores Based on Occupancy Numbers

M. P. Quine and J. Robinson

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Abstract

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.

Article information

Source
Ann. Probab., Volume 12, Number 3 (1984), 794-804.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176993228

Digital Object Identifier
doi:10.1214/aop/1176993228

Mathematical Reviews number (MathSciNet)
MR744234

Zentralblatt MATH identifier
0584.60031

JSTOR
links.jstor.org

Subjects
Primary: 60F05: Central limit and other weak theorems

Keywords
Central limit theorem Berry-Esseen bound occupancy schemes multinomial sums

Citation

Quine, M. P.; Robinson, J. Normal Approximations to Sums of Scores Based on Occupancy Numbers. Ann. Probab. 12 (1984), no. 3, 794--804. doi:10.1214/aop/1176993228. https://projecteuclid.org/euclid.aop/1176993228


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