IDEAS home Printed from https://ideas.repec.org/a/spr/metrik/v82y2019i2d10.1007_s00184-018-0695-7.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00184-018-0695-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00184-018-0695-7?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Gauss Cordeiro & Josemar Rodrigues & Mário Castro, 2012. "The exponential COM-Poisson distribution," Statistical Papers, Springer, vol. 53(3), pages 653-664, August.
    3. Darcy Steeg Morris & Kimberly F. Sellers, 2022. "A Flexible Mixed Model for Clustered Count Data," Stats, MDPI, vol. 5(1), pages 1-18, January.
    4. Imelda Trejo & Nicolas W Hengartner, 2022. "A modified Susceptible-Infected-Recovered model for observed under-reported incidence data," PLOS ONE, Public Library of Science, vol. 17(2), pages 1-23, February.
    5. Fernando Bonassi & Rafael Stern & Cláudia Peixoto & Sergio Wechsler, 2015. "Exchangeability and the law of maturity," Theory and Decision, Springer, vol. 78(4), pages 603-615, April.
    6. Lord, Dominique & Mannering, Fred, 2010. "The statistical analysis of crash-frequency data: A review and assessment of methodological alternatives," Transportation Research Part A: Policy and Practice, Elsevier, vol. 44(5), pages 291-305, June.
    7. Dexter Cahoy & Elvira Di Nardo & Federico Polito, 2021. "Flexible models for overdispersed and underdispersed count data," Statistical Papers, Springer, vol. 62(6), pages 2969-2990, December.
    8. Krivitsky, Pavel N., 2017. "Using contrastive divergence to seed Monte Carlo MLE for exponential-family random graph models," Computational Statistics & Data Analysis, Elsevier, vol. 107(C), pages 149-161.
    9. 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).
    10. Sellers, Kimberly F. & Raim, Andrew, 2016. "A flexible zero-inflated model to address data dispersion," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 68-80.
    11. Mark E. Piatek & Dankmar Böhning, 2024. "Deriving a zero-truncated modelling methodology to analyse capture–recapture data from self-reported social networks," METRON, Springer;Sapienza Università di Roma, vol. 82(2), pages 135-160, August.
    12. Zhou, Can & Jiao, Yan & Browder, Joan, 2019. "K-aggregated transformation of discrete distributions improves modeling count data with excess ones," Ecological Modelling, Elsevier, vol. 407(C), pages 1-1.
    13. Kyle Vincent & Steve Thompson, 2017. "Estimating Population Size With Link-Tracing Sampling," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1286-1295, July.
    14. Rodrigues, Josemar & Balakrishnan, N. & Cordeiro, Gauss M. & de Castro, Mário, 2011. "A unified view on lifetime distributions arising from selection mechanisms," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3311-3319, December.
    15. Rajib Dey & M. Ataharul Islam, 2017. "A conditional count model for repeated count data and its application to GEE approach," Statistical Papers, Springer, vol. 58(2), pages 485-504, June.
    16. Borges, Patrick & Rodrigues, Josemar & Balakrishnan, Narayanaswamy & Bazán, Jorge, 2014. "A COM–Poisson type generalization of the binomial distribution and its properties and applications," Statistics & Probability Letters, Elsevier, vol. 87(C), pages 158-166.
    17. Pattiz, Brian David, 2009. "Count regression models for recreation demand: an application to Clear Lake," ISU General Staff Papers 200901010800002092, Iowa State University, Department of Economics.
    18. Kimberly F. Sellers & Ali Arab & Sean Melville & Fanyu Cui, 2021. "A flexible univariate moving average time-series model for dispersed count data," Journal of Statistical Distributions and Applications, Springer, vol. 8(1), pages 1-12, December.
    19. Rodrigues, Josemar & Bazán, Jorge L. & Suzuki, Adriano K. & Balakrishnan, Narayanaswamy, 2016. "The Bayesian restricted Conway–Maxwell-Binomial model to control dispersion in count data," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 281-288.
    20. Sharad Borle & Peter Boatwright & Joseph B. Kadane & Joseph C. Nunes & Shmueli Galit, 2005. "The Effect of Product Assortment Changes on Customer Retention," Marketing Science, INFORMS, vol. 24(4), pages 616-622, July.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:metrik:v:82:y:2019:i:2:d:10.1007_s00184-018-0695-7. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.