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Limit theorems for some sequential occupancy problems

Published online by Cambridge University Press:  14 July 2016

Svante Janson
Svante Janson*
Affiliation:
Uppsala University
*
∗ Postal address: Department of Mathematics, Uppsala University, Thunbergsvägen 3, S-752–38 Uppsala, Sweden.
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Abstract

Consider n cells into which balls are thrown at random until all but m cells contain at least l + 1 balls each. Asymptotic results when n →∞, m and l held fixed, are given for the number of cells containing exactly k balls and for related random variables.

Keywords

COUPON-COLLECTING
Type
Research Papers
Information
Journal of Applied Probability , Volume 20 , Issue 3 , September 1983 , pp. 545 - 553
Copyright
Copyright © Applied Probability Trust 1983 

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References

[1] Békéssy, A. (1964) On classical occupancy problems II (sequential occupancy). Magy. Tud. Akad. Mat. Kutató Int. Közl. 9, 133–141.Google Scholar
[2] Billingsley, P. (1968) Convergence of Probability Measures. Wiley, New York.Google Scholar
[3] Holst, L. (1981) On sequential occupancy problems. J. Appl. Prob. 18, 435–442.Google Scholar