Let $N$ balls be distributed independently and at random into $n$ boxes. Let $\rho_{nj}$ denote the number of balls in the $j$th box. Let $(c_0, c_1, c_2, \cdots)$ be a sequence of real numbers. Three limit theorems are proved for the sum $\sum^n_{j=1}c_{\rho_{nj}}$ as $N$ and $n$ tend to infinity in such a way that $N/n \rightarrow 0$.
@article{1176994831,
author = {Quine, M. P.},
title = {Three Limit Theorems for Scores Based on Occupancy Numbers},
journal = {Ann. Probab.},
volume = {8},
number = {6},
year = {1980},
pages = { 148-156},
language = {en},
url = {http://dml.mathdoc.fr/item/1176994831}
}
Quine, M. P. Three Limit Theorems for Scores Based on Occupancy Numbers. Ann. Probab., Tome 8 (1980) no. 6, pp. 148-156. http://gdmltest.u-ga.fr/item/1176994831/