The Annals of Applied Probability

Some Limit Theorems on Distributional Patterns of Balls in Urns

Samuel Karlin and Ming-Ying Leung

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Abstract

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.

Article information

Source
Ann. Appl. Probab., Volume 1, Number 4 (1991), 513-538.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1177005836

Digital Object Identifier
doi:10.1214/aoap/1177005836

Mathematical Reviews number (MathSciNet)
MR1129772

Zentralblatt MATH identifier
0753.60014

JSTOR
links.jstor.org

Subjects
Primary: 60F05: Central limit and other weak theorems

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

Citation

Karlin, Samuel; Leung, Ming-Ying. Some Limit Theorems on Distributional Patterns of Balls in Urns. Ann. Appl. Probab. 1 (1991), no. 4, 513--538. doi:10.1214/aoap/1177005836. https://projecteuclid.org/euclid.aoap/1177005836


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