## The Annals of Probability

### Three Limit Theorems for Scores Based on Occupancy Numbers

M. P. Quine

#### Abstract

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 information

Source
Ann. Probab., Volume 8, Number 1 (1980), 148-156.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176994831

Digital Object Identifier
doi:10.1214/aop/1176994831

Mathematical Reviews number (MathSciNet)
MR556421

Zentralblatt MATH identifier
0426.60020

JSTOR