Occupancy and urn models

Abstract

Abstract In this chapter, the general results on Poisson approximation are applied to problems connected with urn models; in particular occupancy problems are studied. Urn models have a long history going back to the early development of probability theory. General references on the subject are Johnson and Kotz (1977), Kolchin, Sevast’yanov and Chistyakov (1978) and the classic Feller (1968). In Section 6.1, the Poisson approximation of the hypergeometric distribution is considered. The number of boxes with given contents in the urn model with a multinomial allocation rule is studied in detail in Section 6.2. In Section 6.3, urn models, negative association and general occupancy problems are discussed. Finally, a matrix occupancy problem is investigated in Section 6.4.