, Volume 82, Issue 2, pp 149–172 | Cite as

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

  • Orasa Anan
  • Dankmar Böhning
  • Antonello MaruottiEmail author


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.


Capture–recapture data Geometric distribution Heterogeneity Count data Variance estimation 



This work is developed under the PRIN2015 supported-project “Environmental processes and human activities: capturing their interactions via statistical methods (EPHASTAT)” funded by MIUR (Italian Ministry of Education, University and Scientific Research). Antonello Maruotti is grateful to the “Centro di Ateneo per la Ricerca e l’Internalizzazione” (LUMSA) for the financial support.

Compliance with ethical standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics and Statistics, Faculty of ScienceThaksin UniversitySongkhlaThailand
  2. 2.Southampton Statistical Sciences Research Institute and Mathematical SciencesUniversity of SouthamptonSouthamptonUK
  3. 3.Dipartimento di Giurisprudenza, Economia, Politica e Lingue ModerneLibera Università Maria Ss. AssuntaRomeItaly
  4. 4.Department of MathematicsUniversity of BergenBergenNorway

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