Use of the ratio plot in capture-recapture estimation

Boehning, Dankmar, Baksh, M. Fazil, Lerdsuwnasri, Rattana and Gallagher, James (2013) Use of the ratio plot in capture-recapture estimation. Journal of Computational and Graphical Statistics, 22, (1), 135-155. (doi:10.1080/10618600.2011.647174).


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Statistical graphics are a fundamental, yet often overlooked, set of components in the repertoire of data analytic tools. Graphs are quick and efficient, yet simple instruments of preliminary exploration of a dataset to understand its structure and to provide insight into influential aspects of inference such as departures from assumptions and latent patterns. In this paper, we present and assess a graphical device for choosing a method for estimating population size in capture-recapture studies of closed populations. The basic concept is derived from a homogeneous Poisson distribution where the ratios of neighboring Poisson probabilities multiplied by the value of the larger neighbor count are constant. This property extends to the zero-truncated Poisson distribution which is of fundamental importance in capture–recapture studies. In practice however, this distributional property is often violated. The graphical device developed here, the ratio plot, can be used for assessing specific departures from a Poisson distribution. For example, simple contaminations of an otherwise homogeneous Poisson model can be easily detected and a robust estimator for the population size can be suggested. Several robust estimators are developed and a simulation study is provided to give some guidance on which should be used in practice. More systematic departures can also easily be detected using the ratio plot. In this paper, the focus is on Gamma-mixtures of the Poisson distribution which leads to a linear pattern (called structured heterogeneity) in the ratio plot. More generally, the paper shows that the ratio plot is monotone for arbitrary mixtures of power series densities.

Item Type: Article
Digital Object Identifier (DOI): doi:10.1080/10618600.2011.647174
ISSNs: 1061-8600 (print)
1537-2715 (electronic)
Keywords: chao and robust and generalized chao estimator, closed population, generalized turing estimator, ord plot, poisson-gamma model, ratio plot, robust turing estimator, structured heterogeneity, turing estimator
Subjects: H Social Sciences > HA Statistics
Divisions : Faculty of Medicine > Primary Care and Population Sciences
Faculty of Social and Human Sciences > Mathematical Sciences > Statistics
Faculty of Social and Human Sciences > Southampton Statistical Sciences Research Institute
ePrint ID: 342535
Accepted Date and Publication Date:
27 March 2013Published
27 December 2011Made publicly available
Date Deposited: 06 Sep 2012 07:42
Last Modified: 31 Mar 2016 14:33

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