Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-21T06:32:14.979Z Has data issue: false hasContentIssue false
  • English
  • Français

Exact Maximum Likelihood Estimate of a Finite Population Size

Capture/Recapture Sequential Sample Data

Published online by Cambridge University Press:  27 July 2009

Jose Galvão Leite ,
Jorge Oishi  and
Carlos Alberto de Bragança Pereira
Jose Galvão Leite
Affiliation:
IME–Universidade de São Paulo, C.P. 20570–01498 São Paulo, Brazil
Jorge Oishi
Affiliation:
IME–Universidade de São Paulo, C.P. 20570–01498 São Paulo, Brazil
Carlos Alberto de Bragança Pereira
Affiliation:
IME–Universidade de São Paulo, C.P. 20570–01498 São Paulo, Brazil
Get access Rights & Permissions [Opens in a new window]

Abstract

Using data obtained by the general capture/recapture sequential sampling process, an exact analytical expression for the maximum likelihood (ML) estimate of the population size, N, is introduced. As a consequence, it is shown that bounded likelihood functions have at most two maxima. For the simple one-by-one case the ML estimate is unique.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 1 , Issue 2 , April 1987 , pp. 225 - 236
Copyright
Copyright © Cambridge University Press 1987

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Chapman, D. C. (1954). The estimation of biological populations. The Annals of Mathematical Statistics 25: 1–15.CrossRefGoogle Scholar
Craig, C. C. (1953). On utilization of marked specimens in estimating the population of flying insects. Biometrika 4: 170–176.CrossRefGoogle Scholar
Darling, D. A. and Robbins, H. (1967). Finding the size of a finite population. The Annals of Mathematical Statistics 38: 1392–1398.CrossRefGoogle Scholar
Darroch, J. N. (1958). The multiple-recapture census I. Estimation of a closed population. Biometrika 45: 343–359.Google Scholar
Darroch, J. N. (1959). The multiple-recapture census II. Estimation when there is immigration or death. Biometrika 46: 336–351.Google Scholar
Good, I. J. (1950). Probability and the Weighing of Evidence, Charles Griffin, London.Google Scholar
Goodman, L. A. (1953). Sequential sampling tagging for population size problems. The Annals of Mathematical Statistics 24: 56–69.CrossRefGoogle Scholar
Freeman, P. R. (1972). Sequential estimation of the size of a population. Biometrika 59: 9–17.CrossRefGoogle Scholar
Isaki, C. T. (1986). Bias of the dual system estimator and some alternatives. Communications in Statistics: Theory and Methods 15(5): 1435–1450.CrossRefGoogle Scholar
Johnson, N. L. and Kotz, S. (1977). Urn Models and Their Applications: An Approach to Modern Discrete Probability Theory, John Wiley, New York.Google Scholar
Jolly, G. M. (1965). Explicit estimates from capture-recapture data with both death and immigration-stochastic model. Biomnetrika 52: 225–247.CrossRefGoogle ScholarPubMed
Jolly, G. M. (1982). Mark-recapture models with parameters constant in time. Biometrika 38: 301–321.CrossRefGoogle ScholarPubMed
Leite, J. G. (1986). Exact estimates of the size of a finite and closed population (in Portuguese). Doctoral Dissertation, São Paulo, Brazil, Universidade de São Paulo, 93p.Google Scholar
Leite, J. G. and Pereira, C. A. de B. (1986). An urn model for the capture/recapture sequential sampling process. Sequential Analysis 6, to appear.Google Scholar
Lewontin, R. C. and Prout, T. (1956). Estimation of the number of different classes in a population. Biometrika 12: 211–223.CrossRefGoogle Scholar
Pollock, K. H., Hines, J. E., and Nichols, J. D. (1985). Goodness-of-fit tests for open capture- recapture models. Biometrika 41: 399–410.CrossRefGoogle Scholar
Robson, D. W. (1969). Mark-recapture methods of population estimation. In: Johnson, and Smith, , eds., New Developments in Survey Sampling, John Wiley, New York.Google Scholar
Samuel, E. (1968). Sequential maximum likelihood estimation of the size of a population. The Annals of Mathematical Statistics 39: 1057–1068.CrossRefGoogle Scholar
Seber, G. A. F. (1962). The multi-sample single recapture census. Biometrika 49: 339–350.CrossRefGoogle Scholar
Seber, G. A. F. (1965). A note on the multiple-recapture census. Biometrika 52: 249–259.CrossRefGoogle ScholarPubMed
Seber, G. A. F. (1982). The Estimation of Animal Abundance and Related Parameters, 2nd ed., Griffin, London.Google Scholar
Seber, G. A. F. (1968). A review of estimating animal abundance. Biometrics 42:267–292.CrossRefGoogle Scholar
Zacks, S. (1981). Parametric Statistical Inference: Basic Theory and Modern Approaches. Pergamon Press, Oxford.Google Scholar
Zacks, S. (1984). Bayes Sequential Estimation of the Size of a Finite Population, São Paulo, Brazil. IME-USP Technical Report 8404, 12p.Google Scholar