ON THE ESTIMATION OF THE SIZE OF A FINITE AND CLOSED POPULATION

In this paper, we consider the problem of estimating the size N of a finite and closed population. using data obtained from capture-recapture experiments. By defining an appropriate model, we investigate the maximum of the likelihood. of the profile likelihood and of an orthogonal adjusted profile likelihood (COX and REID, 1987) function. We show that they all may present infinity as the maximum likelihood estimator of N. This seems to be a characteristic of the likelihood approach in this problem. Further, we present a Bayesian approach with minimum prior information as a way of countering this difficulty. Exact analytical expressions for the posterior modes arc also obtained.