Parameter estimation in the classical occupancy model

Under the classical occupancy model, balls are randomly and independently allocated into cells (by assuming that each arrangement of balls is equally probable) in such a way that the random variable of interest is the empty cell number. In some practical applications the total cell number is known and the target parameter turns out to be the number of balls which is estimated on the basis of the observed empty cell count. For instance, the classical occupancy model is commonly adopted for airborne-microorganism abundance estimation, a topic of central importance in environmental microbiology, in aerobiology and in occupational medicine. The classical occupancy model is also applied to the analysis of US National AIDS surveillance data (which are inflated by duplicate reporting) in order to estimate the true population size of AIDS cases. Since many inaccuracies and misunderstandings are present in applied literature, the aim of the present paper is to introduce a formal analysis of the inferential issues connected with the estimation of the number of balls.