Estimating population size from a removal experiment

A modification of a removal experiment is proposed here to estimate the size of a closed population. The modification is that a known number of marked (or tagged) animals is released into the population before the experiment commences. The removal process is observed for a fixed number of occasions and the removal probabilities are allowed to be time dependent. We derive a maximum likelihood estimator for the population size. The existence and unimodality of the estimator are examined. A simulation study is given on the performance of the estimator under various conditions of the removal process. A goodness of fit test is given to test the homogeneous mixing assumption between the marked and the unmarked ones.