Original Paper

AStA Advances in Statistical Analysis

, Volume 93, Issue 1, pp 61-71

First online:

CAMCR: Computer-Assisted Mixture model analysis for Capture–Recapture count data

  • Ronny KuhnertAffiliated withDivision for Health of Children and Adolescents, Prevention Concepts, Robert Koch-Institute Email author 
  • , Dankmar BöhningAffiliated withQuantitative Biology and Applied Statistics, School of Biological Sciences

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Population size estimation with discrete or nonparametric mixture models is considered, and reliable ways of construction of the nonparametric mixture model estimator are reviewed and set into perspective. Construction of the maximum likelihood estimator of the mixing distribution is done for any number of components up to the global nonparametric maximum likelihood bound using the EM algorithm. In addition, the estimators of Chao and Zelterman are considered with some generalisations of Zelterman’s estimator. All computations are done with CAMCR, a special software developed for population size estimation with mixture models. Several examples and data sets are discussed and the estimators illustrated. Problems using the mixture model-based estimators are highlighted.


CAMCR Capture–recapture Chao’s and Zelterman’s estimator of population size Mixture of truncated Poisson distributions