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An extension of Chao's estimator of population size based on the first three capture frequency counts

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  • Lanumteang, K.
  • Böhning, D.

Abstract

A new estimator for estimating the size of an elusive target population is presented using frequency counts from capture-recapture sampling. The proposed estimator is developed by extending the idea of Chao's estimator using monotonicity of ratios of neighbouring frequency counts under a specific Poisson mixture sampling framework, the Poisson-Gamma mixture or negative binomial. The new estimator is achieved using a simple linear model on the basis of the log-ratio of neighbouring frequency counts as dependent variable which is valid under the Poisson-Gamma mixture. A simulation study is provided to study the performance of the proposed estimator under a variety of heterogeneous Poisson capture probabilities. Confidence interval estimation is done by means of an approximating normal approach and a modified bootstrap method, and was found to perform well. A variety of real data sets were also examined in order to illustrate the use of the proposed method.

Suggested Citation

  • Lanumteang, K. & Böhning, D., 2011. "An extension of Chao's estimator of population size based on the first three capture frequency counts," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2302-2311, July.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:7:p:2302-2311
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    References listed on IDEAS

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    1. Smit, Filip & Reinking, Dick & Reijerse, Maayke, 2002. "Estimating the number of people eligible for health service use," Evaluation and Program Planning, Elsevier, vol. 25(2), pages 101-105, May.
    2. Peter G.M. Van Der Heijden & Maarten Cruyff & Hans C. Van Houwelingen, 2003. "Estimating the Size of a Criminal Population from Police Records Using the Truncated Poisson Regression Model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 57(3), pages 289-304, August.
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    Cited by:

    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.
    2. Durot, Cécile & Huet, Sylvie & Koladjo, François & Robin, Stéphane, 2013. "Least-squares estimation of a convex discrete distribution," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 282-298.
    3. Marco Alfò & Dankmar Böhning & Irene Rocchetti, 2021. "Upper bound estimators of the population size based on ordinal models for capture‐recapture experiments," Biometrics, The International Biometric Society, vol. 77(1), pages 237-248, March.
    4. 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.
    5. Farcomeni, Alessio & Dotto, Francesco, 2021. "A correction to make Chao estimator conservative when the number of sampling occasions is finite," Statistics & Probability Letters, Elsevier, vol. 176(C).

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