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

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 Po...

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Bibliographic Details
Published in:	Computational statistics & data analysis Vol. 55; no. 7; pp. 2302 - 2311
Main Authors:	Lanumteang, K., Böhning, D.
Format:	Journal Article
Language:	English
Published:	Amsterdam Elsevier B.V 01-07-2011 Elsevier
Series:	Computational Statistics & Data Analysis
Subjects:	Approximation Binomials Capture–recapture methods Chao’s estimator Counting Estimation of population size Estimation of population size Capture-recapture methods Horvitz-Thompson estimator Chao's estimator Homogeneous and heterogeneous Poisson models Negative binomial Estimators Exact sciences and technology General topics Homogeneous and heterogeneous Poisson models Horvitz–Thompson estimator Mathematical models Mathematics Multivariate analysis Negative binomial Neighbouring Numerical analysis Numerical analysis. Scientific computation Numerical methods in probability and statistics Parametric inference Probability and statistics Sampling Sciences and techniques of general use Statistics Horvitz–Thompson estimator Chao’s estimator Homogeneous and heterogeneous Poisson models Negative binomial Capture–recapture methods Estimation of population size Chaos Horvitz Thompson estimator Capture-recapture methods Chao's estimator Non parametric estimation Dependent variable Statistical simulation Negative binomial distribution Linear model Bootstrap Jackknife method Sampling Homogeneous and heterogeneous Poisson Mixed distribution models Data analysis Horvitz-Thompson estimator Statistical estimation Confidence interval Statistical computation Capture recapture method Capture probability Population size Resampling method
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Summary:	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.
Bibliography:	ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23
ISSN:	0167-9473 1872-7352
DOI:	10.1016/j.csda.2011.01.017