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December, 1977 Some Asymptotic Results for Occupancy Problems
Lars Holst
Ann. Probab. 5(6): 1028-1035 (December, 1977). DOI: 10.1214/aop/1176995671


Suppose $n$ balls are placed into $N$ cells with arbitrary probabilities. Limit distributions for the number of empty cells are considered when $N \rightarrow \infty$ and $n \rightarrow \infty$ in such a way that $n/N \rightarrow \infty$. Limit distributions for the number of balls to achieve exactly $b$ empty cells are obtained for $N \rightarrow \infty$ with $b$ fixed and for $b \rightarrow \infty$ with $b/N \rightarrow 0$.


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Lars Holst. "Some Asymptotic Results for Occupancy Problems." Ann. Probab. 5 (6) 1028 - 1035, December, 1977.


Published: December, 1977
First available in Project Euclid: 19 April 2007

zbMATH: 0372.60034
MathSciNet: MR443027
Digital Object Identifier: 10.1214/aop/1176995671

Primary: 60F05
Secondary: 60C05

Keywords: coupon collectors problem , limit theorems , occupancy problems

Rights: Copyright © 1977 Institute of Mathematical Statistics

Vol.5 • No. 6 • December, 1977
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