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

Authors
  • Anan, Orasa1
  • Böhning, Dankmar2
  • Maruotti, Antonello3, 4
  • 1 Thaksin University, Department of Mathematics and Statistics, Faculty of Science, Songkhla, Thailand , Songkhla (Thailand)
  • 2 University of Southampton, Southampton Statistical Sciences Research Institute and Mathematical Sciences, Southampton, UK , Southampton (United Kingdom)
  • 3 Libera Università Maria Ss. Assunta, Dipartimento di Giurisprudenza, Economia, Politica e Lingue Moderne, Rome, Italy , Rome (Italy)
  • 4 University of Bergen, Department of Mathematics, Bergen, Norway , Bergen (Norway)
Type
Published Article
Journal
Metrika
Publisher
Springer Berlin Heidelberg
Publication Date
Nov 12, 2018
Volume
82
Issue
2
Pages
149–172
Identifiers
DOI: 10.1007/s00184-018-0695-7
Source
Springer Nature
Keywords
License
Yellow

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.

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