Use of the Ratio Plot in Capture–Recapture Estimation

References

• Baksh, M.F., Böhning, D., and Lerdsuwansri, R. (2011), “An Extension of an Over-Dispersion Test for Count Data,” Computational Statistics and Data Analysis, 55, 466–474.
   Web of Science ®Google Scholar
• Böhning, D. (2008), “A Simple Variance Formula for Population Size Estimators by Conditioning,” Statistical Methodology, 5, 410–423.
   Google Scholar
• Böhning, D., and Del Rio Vilas, V.J. (2008), “Estimating the Hidden Number of Scrapie Affected Holdings in Great Britain Using a Simple, Truncated Count Model Allowing for Heterogeneity,” Journal of Agricultural, Biological and Environmental Statistics, 13, 1–22.
   Web of Science ®Google Scholar
• Böhning, D., and Kuhnert, R. (2006), “The Equivalence of Truncated Count Mixture Distributions and Mixtures of Truncated Count Distributions,” Biometrics, 62, 1207–1215.
   PubMed Web of Science ®Google Scholar
• Böhning, D., and Schön, D. (2005), “Nonparametric Maximum Likelihood Estimation of the Population Size Based Upon the Counting Distribution,” Journal of the Royal Statistical Society, Series C, 54, 721–737.
   Web of Science ®Google Scholar
• Bunge, J., and Fitzpatrick, M. (1993), “Estimating the Number of Species: A Review,” Journal of the American Statistical Association, 88, 364–373.
   Web of Science ®Google Scholar
• Chao, A. (1987), “Estimating the Population Size for Capture–Recapture Data With Unequal Catchability,” Biometrics, 43, 783–791.
   PubMed Web of Science ®Google Scholar
• ——— (1989), “Estimating Population Size for Sparse Data in Capture–Recapture Experiments,” Biometrics, 45, 427–438.
   Web of Science ®Google Scholar
• Chao, A., and Bunge, J. (2002), “Estimating the Number of Species in a Stochastic Abundance Model,” Biometrics, 58, 531–539.
   PubMed Web of Science ®Google Scholar
• Chao, A., and Huggins, R.M. (2005), “Modern Closed-Population Capture–Recapture Models,” in Handbook of Capture–Recapture Analysis, eds. S. C. Amstrup, T. L. McDonald, and B. F. J. Manly, Princeton: Princeton University Press, pp. 58–87.
   Google Scholar
• Chao, A., Tsay, P.K., Lin, S.H., Shau, W.Y., and Chao, D.Y. (2001), “Tutorial in Biostatistics: The Applications of Capture–Recapture Models to Epidemiological Data,” Statistics in Medicine, 20, 3123–3157.
   PubMed Web of Science ®Google Scholar
• Cullen, M.J., Walsh, J., Nicholson, L. V.B., and Harris, J.B. (1990), “Ultrastructural Localization of Dystrophin in Human Muscle by Using Gold Immunolabelling,” Proceedings of the Royal Society of London, Series B, 20, 197–210.
   Web of Science ®Google Scholar
• Dorazio, R.M., and Royle, J.A. (2005), “Mixture Models for Estimating the Size of a Closed Population When Capture Rates Vary Among Individuals,” Biometrics, 59, 351–364.
   Web of Science ®Google Scholar
• Friendly, M. (2000), Visualizing Categorical Data, Cary, NC: SAS Insitute.
   Google Scholar
• Gart, J.J. (1970), “Some Simple Graphically Oriented Statistical Methods for Discrete Data,” in Random Counts in Scientific Work, Volume 1: Random Counts in Models and Structures, ed. G. P. Patil, University Park, PA: The Pennsylvania State University Press, pp. 171–191.
   Google Scholar
• Good, I.J. (1953), “On the Population Frequencies of Species and the Estimation of Population Parameters,” Biometrika, 40, 237–264.
   Web of Science ®Google Scholar
• Hay, G., and Smit, F. (2003), “Estimating the Number of Drug Injectors From Needle Exchange Data,” Addiction Research and Theory, 11, 235–243.
   Web of Science ®Google Scholar
• Hoaglin, D.C. (1980), “A Poissonness Plot,” The American Statistician, 34, 146–149.
   Web of Science ®Google Scholar
• Hoaglin, D. C., and Tukey, J. W. (1985), “Checking the Shape of Discrete Distributions” in Exploring Data Tables, Trends, and Shapes, eds. D. C. Hoaglin, F. Mosteller, and J. W. Tukey, Hoboken: Wiley, pp. 345–416.
   Google Scholar
• Holzmann, H., Munk, A., and Zucchini, W. (2006), “On Identifiability in Capture–Recapture Models,” Biometrics, 62, 934–939.
   PubMed Web of Science ®Google Scholar
• Hser, Y.I. (1993), “Population Estimates of Intravenous Drug Users and HIV Infection in Los Angeles County,” International Journal of Addictions, 28, 695–709.
   PubMed Web of Science ®Google Scholar
• Kuhnert, R., Del Rio Vilas, V.J., Gallagher, J., and Böhning, D. (2008), “A Bagging-Based Correction for the Mixture Model Estimator of Population Size,” Biometrical Journal, 50, 993–1005.
   PubMed Web of Science ®Google Scholar
• Link, W.A. (2003), “Nonidentifiability of Population Size From Capture–Recapture Data With Heterogeneous Detection Probabilities,” Biometrics, 59, 1123–1130.
   PubMed Web of Science ®Google Scholar
• ——— (2006), “Response to a Paper by Holzmann, Munk and Zucchini,” Biometrics, 62, 936–939.
   Google Scholar
• Mao, C.X. (2006), “Inference on the Number of Species Through Geometric Lower Bounds,” Journal of the American Statistical Association, 101, 1663–1670.
   Web of Science ®Google Scholar
• ——— (2007), “Estimating Population Sizes for Capture–Recapture Sampling With Binomial Mixtures,” Computational Statistics and Data Analysis, 51, 5211–5219.
   Web of Science ®Google Scholar
• Mao, C.X., and Lindsay, B.G. (2007), “Estimating the Number of Classes,” The Annals of Statistics, 35, 917–930.
   Web of Science ®Google Scholar
• Matthews, J. N.S., and Appleton, D.R. (1993), “An Application of the Truncated Poisson Distribution to Immunogold Assay,” Biometrics, 49, 617–621.
   PubMed Web of Science ®Google Scholar
• Moore, P.G. (1952), “The Estimation of the Poisson Parameter From a Truncated Distribution,” Biometrika, 39, 247–251.
   Web of Science ®Google Scholar
• Ord, J.K. (1967), “Graphical Methods for a Class of Distributions,” Journal of the Royal Statistical Society, Series A, 130, 232–238.
   Web of Science ®Google Scholar
• Pawitan, Y. (2001), In All Likelihood: Statistical Modelling and Inference Using Likelihood, Oxford: Oxford University Press.
   Google Scholar
• Pledger, S.A. (2005), “The Performance of Mixture Models in Heterogeneous Closed Population Capture–Recapture,” Biometrics, 61, 868–876.
   PubMed Web of Science ®Google Scholar
• van der Heijden, P. G.M., Bustami, R., Cruyff, M., Engbersen, G., and van Houwelingen, H.C. (2003a), “Point and Interval Estimation of the Population Size Using the Truncated Poisson Regression Model,” Statistical Modelling, 3, 305–322.
   Web of Science ®Google Scholar
• van der Heijden, P. G.M., Cruyff, M., and van Houwelingen, H.C. (2003b), “Estimating the Size of a Criminal Population From Police Records Using the Truncated Poisson Regression Model,” Statistica Neerlandica, 57, 1–16.
   Web of Science ®Google Scholar
• Wang, J.-P., and Lindsay, B.G. (2005), “A Penalized Nonparametric Maximum Likelihood Approach to Species Richness Estimation,” Journal of the American Statistical Association, 100, 942–959.
   Web of Science ®Google Scholar
• ——— (2008), “An Exponential Partial Prior for Improving Nonparametric Maximum Likelihood Estimation in Mixture Models,” Statistical Methodology, 5, 30–45.
   Google Scholar
• Zelterman, D. (1988), “Robust Estimation in Truncated Discrete Distributions With Applications to Capture–Recapture Experiments,” Journal of Statistical Planning and Inference, 18, 225–237.
   Web of Science ®Google Scholar