## The Annals of Probability

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

### Normal Approximations to Sums of Scores Based on Occupancy Numbers

#### 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