Abstract
In the present paper, we consider an equiprobable allocation urn model with m urns of limited capacity and study the distribution of the number of overflown urns and the number of excess balls (i.e those assigned to already filled up urns) after n balls have been assigned. The exact distribution of the variables of interest are studied by a Markov chain imbedding method; a Poisson and compound Poisson approximation is discussed as well along with estimates of their rates of convergence. Certain limit laws as n, m→∞ are also established under appropriate conditions on n, m and urns’ capacities.
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