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Limit Theorems for Some Occupancy and Sequential Occupancy Problems

Lars Holst
The Annals of Mathematical Statistics
Vol. 42, No. 5 (Oct., 1971), pp. 1671-1680
Stable URL: http://www.jstor.org/stable/2240290
Page Count: 10
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Limit Theorems for Some Occupancy and Sequential Occupancy Problems
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Abstract

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.

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