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Population size estimation and heterogeneity in capture–recapture data: a linear regression estimator based on the Conway–Maxwell–Poisson distribution

Author

Listed:
  • Orasa Anan

    (University of Southampton)

  • Dankmar Böhning

    (University of Southampton)

  • Antonello Maruotti

    (Libera Universitá Maria Ss. Assunta
    University of Southampton)

Abstract

The purpose of the study is to estimate the population size under a truncated count model that accounts for heterogeneity. The proposed estimator is based on the Conway–Maxwell–Poisson distribution. The benefit of using the Conway–Maxwell–Poisson distribution is that it includes the Bernoulli, the Geometric and the Poisson distributions as special cases and, furthermore, allows for heterogeneity. Parameter estimates can be obtained by exploiting the ratios of successive frequency counts in a weighted linear regression framework. The results of the comparisons with Turing’s, the maximum likelihood Poisson, Zelterman’s and Chao’s estimators reveal that our proposal can be beneficially used. Furthermore, our proposal outperforms its competitors under all heterogeneous settings. The empirical examples consider the homogeneous case and several heterogeneous cases, each with its own features, and provide interesting insights on the behavior of the estimators.

Suggested Citation

  • Orasa Anan & Dankmar Böhning & Antonello Maruotti, 2017. "Population size estimation and heterogeneity in capture–recapture data: a linear regression estimator based on the Conway–Maxwell–Poisson distribution," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(1), pages 49-79, March.
    • Handle: RePEc:spr:stmapp:v:26:y:2017:i:1:d:10.1007_s10260-016-0358-7
    DOI: 10.1007/s10260-016-0358-7
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    References listed on IDEAS

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    1. Chun-Huo Chiu & Yi-Ting Wang & Bruno A. Walther & Anne Chao, 2014. "An improved nonparametric lower bound of species richness via a modified good–turing frequency formula," Biometrics, The International Biometric Society, vol. 70(3), pages 671-682, September.
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    4. Robert M. Dorazio & J. Andrew Royle, 2003. "Mixture Models for Estimating the Size of a Closed Population When Capture Rates Vary among Individuals," Biometrics, The International Biometric Society, vol. 59(2), pages 351-364, June.
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