International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 28, Pages 1771-1782

A zero-inflated occupancy distribution: exact results and Poisson convergence

Nikolai Kolev1 and Ljuben Mutafchiev2

1Department of Statistics, Institute of Mathematics and Statistics, University of São Paulo, CP 66281, São Paulo 05311-970, Brazil
2American University in Bulgaria, Blagoevgrad 2700, Bulgaria

Received 2 September 2002

Copyright © 2003 Nikolai Kolev and Ljuben Mutafchiev. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We introduce the generalized zero-inflated allocation scheme of placing n labeled balls into N labeled cells. We study the asymptotic behavior of the number of empty cells when (n,N) belongs to the “right” and “left” domain of attraction. An application to the estimation of characteristics of agreement among a set of raters which independently classify subjects into one of two categories is also indicated. The case when a large number of raters acts following the zero-inflated binomial law with small probability for positive diagnosis is treated using the zero-inflated Poisson approximation.