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November, 1991 Some Limit Theorems on Distributional Patterns of Balls in Urns
Samuel Karlin, Ming-Ying Leung
Ann. Appl. Probab. 1(4): 513-538 (November, 1991). DOI: 10.1214/aoap/1177005836


In an independent, equiprobable allocation urn model, there are various Poisson and normal limit laws for the occupancy of single urns. Applying the Chen-Stein method, we obtain Poisson, compound Poisson and multivariate Poisson limit laws, together with estimates of their rates of convergence, for the number of chunks of $\kappa$ (fixed) adjacent urns occupied by certain numbers of balls distributed in some specified patterns. Several related results on occupancy, waiting time and spacings at certain random times are also presented.


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Samuel Karlin. Ming-Ying Leung. "Some Limit Theorems on Distributional Patterns of Balls in Urns." Ann. Appl. Probab. 1 (4) 513 - 538, November, 1991.


Published: November, 1991
First available in Project Euclid: 19 April 2007

zbMATH: 0753.60014
MathSciNet: MR1129772
Digital Object Identifier: 10.1214/aoap/1177005836

Primary: 60F05

Keywords: Ball-in-urn models , Chen-Stein method , occupancy distributions , Poisson approximations

Rights: Copyright © 1991 Institute of Mathematical Statistics


Vol.1 • No. 4 • November, 1991
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