Exact and asymptotic inference for the size of a population

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Abstract
A population contains an unknown number N of members. These could be animals in a closed population or errors in a manuscript. There are K counters, trappers or proof readers, say. The unknown detection probabilities vary with the counter but not with the member of the population. We prove that the likelihood has a unique local maximum and that our iterative algorithm always converges to it. We find exact confidence intervals for the population size N and normal approximations to them. Our normal approximation is much closer to the exact values than the values, in the literature, using the maximum likelihood estimator and its estimated standard error. A simulation study of confidence interval coverage shows that the coverage frequencies for our method are much closer to the probabilities than are those for the existing method.

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