American Review of Mathematics and Statistics

A Review of Methods for Point and Interval Estimation of Population Size in Capture-Recapture Studies
Carlo Cosenza; Lynn Eudey, PhD; Joshua Kerr, PhD; Bruce Trumbo, PhD

Abstract
Estimates of population size in a classical capture-recapture experiment are obtained by method of moments and maximum likelihood estimation. Exact confidence intervals using the hypergeometric distribution (the general method) and approximate confidence intervals using the normal approximation and separately, the binomial approximation are illustrated. Estimates of coverage probabilities are explored using the hypergeometric distribution for the general method and for both approximate methods. Bayesian methods of interval estimation are also illustrated. The computer software R is used to do the intensive computation and make figures. R-code for the methods is provided in text boxes. The capture-recapture study provides a unique setting in which to explore both traditional and Bayesian estimation methods using a discrete distribution with a discrete prior.

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