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.
Publié le : 1984-08-14
Classification:
Central limit theorem,
Berry-Esseen bound,
occupancy schemes,
multinomial sums,
60F05
@article{1176993228,
author = {Quine, M. P. and Robinson, J.},
title = {Normal Approximations to Sums of Scores Based on Occupancy Numbers},
journal = {Ann. Probab.},
volume = {12},
number = {4},
year = {1984},
pages = { 794-804},
language = {en},
url = {http://dml.mathdoc.fr/item/1176993228}
}
Quine, M. P.; Robinson, J. Normal Approximations to Sums of Scores Based on Occupancy Numbers. Ann. Probab., Tome 12 (1984) no. 4, pp. 794-804. http://gdmltest.u-ga.fr/item/1176993228/