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On restricted and pseudo-contagious occupancy distributions

Published online by Cambridge University Press:  14 July 2016

Ch. A. Charalambides
Ch. A. Charalambides*
Affiliation:
University of Athens
*
∗ Postal address: Statistical Unit, University of Athens, Panepistemiopolis, Athens 621, Greece.
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Abstract

Consider m distinguishable urns with k distinguishable cells each and suppose that n indistinguishable balls are randomly allocated into these urns. When the capacity of each cell is limited to one ball (restricted occupancy) or unlimited (pseudo-contagious occupancy) and empty urns are not permitted, the probability function and factorial moments of the number Mt = Mt (n, m, k) of urns containing exactly t balls are expressed in terms of numbers related to the Stirling numbers. The limiting distributions of Mt = Mt (n, m, k) when k → 0 or k →∞ are derived; these distributions are expressed in terms of the Stirling numbers of the first and second kind respectively. Moreover a modification of the occupancy models of Barton and David is shown to lead to the preceding distributions.

Keywords

RESTRICTED OCCUPANCYPSEUDO-CONTAGIOUS OCCUPANCYZERO-TRUNCATED DISTRIBUTIONS
Type
Short Communications
Information
Journal of Applied Probability , Volume 20 , Issue 4 , December 1983 , pp. 872 - 876
Copyright
Copyright © Applied Probability Trust 1983 

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