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Biometrika 1984 71(1):27-33; doi:10.1093/biomet/71.1.27
© 1984 by Biometrika Trust
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Statistical inference for Poisson and multinomial models for capture-recapture experiments

R. L. SANDLAND and R. M. CORMACK

SIRO, Division of Mathematics and Statistics Cronulla, New South Wales, Australia
Department of Statistics, University of St Andrews St Andrews, U.K.

The classical multinomial model used for estimating the size of a closed population is compared to the highly flexible Poisson models introduced by Cormack (1981). The multinomial model, and generalizations of it which allow for dependence between samples, may be obtained from that of Cormack by conditioning on the population size. The maximum likelihood estimators for N, the population size, and {theta}, the vector of parameters describing the capture process, are the same in both models. Completely general formulae for the asymptotic variances of the maximum likelihood estimates of N for both models are given. The substantial differences between the variances under the two models are discussed. Hypotheses concerning {theta} may be tested using the log likelihood ratio; the procedures which result from both models are asymptotically equivalent under the null hypothesis but differ in power under the alternative.

Key Words: Capture-recapture experiment • OLIM • Likelihood ratio test • Log linear model • Maximum likelihood estimation • Population size estimate.


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