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February, 1980 Three Limit Theorems for Scores Based on Occupancy Numbers
M. P. Quine
Ann. Probab. 8(1): 148-156 (February, 1980). DOI: 10.1214/aop/1176994831


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 $N/n \rightarrow 0$.


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M. P. Quine. "Three Limit Theorems for Scores Based on Occupancy Numbers." Ann. Probab. 8 (1) 148 - 156, February, 1980.


Published: February, 1980
First available in Project Euclid: 19 April 2007

zbMATH: 0426.60020
MathSciNet: MR556421
Digital Object Identifier: 10.1214/aop/1176994831

Primary: 60F05

Keywords: degenerate , limit theorems , normal , occupancy numbers , Poisson

Rights: Copyright © 1980 Institute of Mathematical Statistics

Vol.8 • No. 1 • February, 1980
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