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On the Turing estimator in capture–recapture count data under the geometric distribution

Author

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  • Orasa Anan

    (Thaksin University)

  • Dankmar Böhning

    (University of Southampton)

  • Antonello Maruotti

    (Libera Università Maria Ss. Assunta
    University of Bergen)

Abstract

We introduce an estimator for an unknown population size in a capture–recapture framework where the count of identifications follows a geometric distribution. This can be thought of as a Poisson count adjusted for exponentially distributed heterogeneity. As a result, a new Turing-type estimator under the geometric distribution is obtained. This estimator can be used in many real life situations of capture–recapture, in which the geometric distribution is more appropriate than the Poisson. The proposed estimator shows a behavior comparable to the maximum likelihood one, on both simulated and real data. Its asymptotic variance is obtained by applying a conditional technique and its empirical behavior is investigated through a large-scale simulation study. Comparisons with other well-established estimators are provided. Empirical applications, in which the population size is known, are also included to further corroborate the simulation results.

Suggested Citation

  • Orasa Anan & Dankmar Böhning & Antonello Maruotti, 2019. "On the Turing estimator in capture–recapture count data under the geometric distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(2), pages 149-172, March.
    • Handle: RePEc:spr:metrik:v:82:y:2019:i:2:d:10.1007_s00184-018-0695-7
    DOI: 10.1007/s00184-018-0695-7
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    References listed on IDEAS

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    1. Galit Shmueli & Thomas P. Minka & Joseph B. Kadane & Sharad Borle & Peter Boatwright, 2005. "A useful distribution for fitting discrete data: revival of the Conway–Maxwell–Poisson distribution," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(1), pages 127-142, January.
    2. Pedro Puig & Célestin C. Kokonendji, 2018. "Non†parametric Estimation of the Number of Zeros in Truncated Count Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 45(2), pages 347-365, June.
    3. Chris J. Lloyd & Donald J. Frommer, 2004. "Regression‐based estimation of the false negative fraction when multiple negatives are unverified," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 53(4), pages 619-631, November.
    4. Wen-Han Hwang & Richard Huggins, 2005. "An examination of the effect of heterogeneity on the estimation of population size using capture-recapture data," Biometrika, Biometrika Trust, vol. 92(1), pages 229-233, March.
    5. Sa-aat Niwitpong & Dankmar Böhning & Peter Heijden & Heinz Holling, 2013. "Capture–recapture estimation based upon the geometric distribution allowing for heterogeneity," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(4), pages 495-519, May.
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    Cited by:

    1. Jiménez-Gamero, M.D. & Alba-Fernández, M.V., 2021. "A test for the geometric distribution based on linear regression of order statistics," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 186(C), pages 103-123.

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