Analysis of a multiple-recapture census by computing conditional probabilities

In a multiple-recapture census of a closed population using fixed sample sizes, the total number of different animals captured during the census is a sufficient statistic for the population size. Conditional on the population size, the exact probability distribution of this sufficient statistic may be calculated and an algorithm for doing this is given. Standard techniques are applied to describe methods for using the conditional probabilities to form median and interval estimates of the population size. The methods are illustrated with examples.