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Limit Theorems for Some Occupancy and Sequential Occupancy Problems
The Annals of Mathematical Statistics
Vol. 42, No. 5 (Oct., 1971), pp. 1671-1680
Published by: Institute of Mathematical Statistics
Stable URL: http://www.jstor.org/stable/2240290
Page Count: 10
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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 → ∞, so that n2/N → ∞ and n/N → 0. This result completes some theorems given by Chistyakov (1964), (1967). Limiting distributions of the number of falls to achieve aN + 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.
The Annals of Mathematical Statistics © 1971 Institute of Mathematical Statistics