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October, 1971 Limit Theorems for Some Occupancy and Sequential Occupancy Problems
Lars Holst
Ann. Math. Statist. 42(5): 1671-1680 (October, 1971). DOI: 10.1214/aoms/1177693165


Consider a situation in which balls are falling into $N$ cells with arbitrary probabilities. A limiting distribution for the number of occupied cells after $n$ falls is obtained, when $n$ and $N \rightarrow \infty$, so that $n^2/N \rightarrow \infty$ and $n/N \rightarrow 0$. This result completes some theorems given by Chistyakov (1964), (1967). Limiting distributions of the number of falls to achieve $a_N + 1$ occupied cells are obtained when $\lim \sup a_N/N < 1$. These theorems generalize theorems given by Baum and Billingsley (1965), and David and Barton (1962), when the balls fall into cells with the same probability for every cell.


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Lars Holst. "Limit Theorems for Some Occupancy and Sequential Occupancy Problems." Ann. Math. Statist. 42 (5) 1671 - 1680, October, 1971.


Published: October, 1971
First available in Project Euclid: 27 April 2007

zbMATH: 0231.60022
MathSciNet: MR343347
Digital Object Identifier: 10.1214/aoms/1177693165

Rights: Copyright © 1971 Institute of Mathematical Statistics


Vol.42 • No. 5 • October, 1971
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