The Annals of Applied Probability

Some Limit Theorems on Distributional Patterns of Balls in Urns

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

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