The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 1, Number 4 (1991), 513-538.
Some Limit Theorems on Distributional Patterns of Balls in Urns
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.
Ann. Appl. Probab., Volume 1, Number 4 (1991), 513-538.
First available in Project Euclid: 19 April 2007
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Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60F05: Central limit and other weak theorems
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