59
Views
3
CrossRef citations to date
0
Altmetric
Original Articles

A stepwise Bayesian estimator for the total number of distinct species in finite populations: Sampling by elements

Pages 651-670 | Published online: 02 Aug 2010

  • Andreawartha , H. G. 1961 . Introduction of the Study of Animal Populations , Chicago : University of Chicago Press .
  • Berger , J. O. 1985 . Statistical Decision Theory and Bayesian Analysis, , 2nd edn , New York : Springer Verlag .
  • Betroà , B. and Zielinski , R. 1987 . A Monte Carlo study of a Bayesian decision rule concerning the number of diVerent values of a discrete random variable . Communication Statistics Simulation Computing , 16 (4) : 925 – 938 .
  • Boender , C. G. E. and Rinnooy Kan , A. H. G. 1983 . A Bayesian analysis of the number of cells of a multinomial distribution . The Statistician , 32 : 240 – 248 .
  • Boender , C. G. E. and Rinnooy Kan , A. H. G. 1987 . A multinomial Bayesian approach to the estimation of population and vocabulary size . Biometrika , 74 : 849 – 856 .
  • Boender , C. G. E. and Zielinski , R. 1985 . A sequential Bayesian approach to estimating the dimension of a multinomial distribution . Sequential Methods in Statistics , 16 : 37 – 42 .
  • Bunge , J. and Fitzpatrick , M. 1993 . Estimating the number of species: a review . Journal of the American Statistical Association , 88 : 364 – 373 .
  • Bunge , J. , Fitzpatrick , M. and Handley , J. 1995 . Comparison of three estimators of the number of species . Journal of Applied Statistics , 22 : 45 – 58 .
  • Chao , A. and Lee , S.-M. 1992 . Estimating the number of classes via sample coverage . Journal of the American Society , 87 : 210 – 217 .
  • Driml , M. and Ullrich , M. 1967 . Maximum likelihood estimate of the number of types . Acta Technica CSAV , 3 : 300 – 303 .
  • Efron , B. and Thisted , R. 1976 . Estimating the species: how many words did Shakespeare know? . Biometrika , 63 : 435 – 447 .
  • Emigh , T. H. 1983 . On the number of observed classes from a multinomial distribution . Biometrics , 39 : 485 – 491 .
  • Engen , S. 1978 . Stochastic Abundance Models , New York : John Wiley & Sons .
  • Esty , W. W. 1985 . Estimation of the number of classes in a population and the coverage of a sample . Mathematical Scientist , 10 : 41 – 50 .
  • Fisher , R. A. , Corbet , A. S. and Williams , C. B. 1943 . The relation between the number of species and the number of individuals in a random sample of an animal population . Journal Animal Ecology , 12 : 42 – 58 .
  • Good , I. J. and Toulmin , G. H. 1956 . The number of new species, and the increase in population coverage, when a sample is increased . Biometrika , 43 : 45 – 63 .
  • Goodman , L. A. 1949 . On the estimation of the number of classes in a population . Annals of Mathematical Statistics , 20 : 572 – 579 .
  • Gray , H. L. and Schucany , W. R. 1972 . The Generalized Jackknife Statistic , New York : Marcel Dekker .
  • Haas , P. J. and Stokes , L. 1998 . Estimating the number of classes in a finite population . Journal of the American Statistical Association , 93 : 1475 – 1487 .
  • Harris , B. 1968 . Statistical inference in the classical occupancy problem unbiased estimation of the number of classes . Journal of the American Statistical Association , 63 : 837 – 847 .
  • Hill , B. M. 1979 . Posterior moments of the number of species in a finite population and the posterior probability of finding a new species . Journal of the American Statistical Association , 74 : 668 – 673 .
  • Hsuan , F. C. 1979 . A stepwise Bayesian procedure . Annals of Statistics , 7 : 860 – 868 .
  • Janardan , K. G. and Schaeffer , D. J. 1981 . Application of discrete distributions for estimating the number of organic compounds in water . Statistical Distributions in Scientific Work , 6 : 79 – 94 .
  • Lewins , W. A. and Joanes , D. N. 1984 . Bayesian estimation of the number of species . Biometrics , 40 : 323 – 328 .
  • Lewontin , R. C. and Pront , T. 1956 . Estimation of the number of diVerent classes in a population . Biometrics , 12 : 211 – 223 .
  • Lincoln , F. C. 1930 . Calculating waterfowl abundance on the basis of banding returns . U.S. Department of Agricultural Circular , 118 : 1 – 4 .
  • Ludwig , J. A. and Reynolds , J. F. 1988 . Statistical Ecology , New York : John Wiley & Sons .
  • McNeil , D. 1973 . Estimating an author's vocabulary . Journal of American Statistical Association , 68 : 92 – 96 .
  • Meeden , G. and Ghosh , M. 1981 . Admissibility in finite problems . Annals of Statistics , 9 : 846 – 852 .
  • Mingoti , S. A. 1999 . Bayesian estimator for the total number of distinct species when quadrat sampling is used . Journal of Applied Statistics , 26 (4) : 463 – 477 .
  • Mingoti , S. A. and Meeden , G. 1992 . Estimating the total number of distinct species using presence and absence data . Biometrics , 48 : 863 – 875 .
  • Otis , D. , Burnhan , K. P. , White , G. C. and Anderson , D. R. 1978 . Statistical inference from capture data on closed populations . Wildlife Monographs , 62 : 1 – 135 .
  • Petersen , G. G. J. 1896 . The yearly immigration of young plaice into the Limfjord from the German sea . Report of Danish Biology Statistics , 6 : 1 – 48 .
  • Pielou , E. C. 1977 . Mathematical Ecology , New York : John Wiley & Sons .
  • Seber , G. A. F. 1982 . The estimation of Animal Abundance and Related Parameters, , 2nd edn , London : GriYn .
  • Seber , G. A. F. 1986 . A review of estimating animal abundance . Biometrics , 42 : 267 – 292 .
  • Seber , G. A. F. 1992 . A review of estimating animal abundance II . International Statistical Review , 60 (2) : 129 – 166 .
  • Simon , J. , Bruce , P. and Oswald , T. 1995 . Resampling stats user's guide , Virginia : Resampling Stats, Inc. .
  • Sichel , H. 1986 . Parameter estimation for a word frequency distribution based on occupancy theory . Communications in Statistics - Theory and Methods , 15 : 935 – 949 .
  • Taylor , L. R. , Woiwod , I. P. and Perry , J. N. 1979 . The negative binomial as a dynamic ecological model for aggregation, and the density dependence of k . Journal of Animal Ecology , 48 : 289 – 304 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.