Title:
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Comparing the suitability of two factors for stratification in estimating diversity (English) |
Author:
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Gil, María Angeles |
Language:
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English |
Journal:
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Kybernetika |
ISSN:
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0023-5954 |
Volume:
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27 |
Issue:
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6 |
Year:
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1991 |
Pages:
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495-505 |
. |
Category:
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math |
. |
MSC:
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62B10 |
MSC:
|
62D05 |
MSC:
|
62F05 |
MSC:
|
62P10 |
MSC:
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92D40 |
idZBL:
|
Zbl 0745.62007 |
idMR:
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MR1150939 |
. |
Date available:
|
2009-09-24T18:28:29Z |
Last updated:
|
2012-06-05 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/124296 |
. |
Reference:
|
[1] G. P. Basharin: On a statistical estimate for the entropy of a sequence of independent random variables.Theory Probab. Appl. 4 (1959), 333 - 336. Zbl 0092.36701, MR 0127457 |
Reference:
|
[2] T. N. Bhargava, P. H. Doyle: A geometric study of diversity.J. Theoret. Biology 43 (1974), 241-251. |
Reference:
|
[3] T. N. Bhargava, V. R. R. Uppuluri: Sampling distribution of Gini's index of diversity.Appl. Math. Comput. 3 (1977), 1-24. Zbl 0403.62018, MR 0436416 |
Reference:
|
[4] P. J. Bickel, K. A. Doksum: Mathematical Statistics.Holden-Day, Inc., Oakland 1977. Zbl 0403.62001, MR 0443141 |
Reference:
|
[5] Z. W. Birnbaum: Introduction to Probability and Mathematical Statistics.Harper & Row, New York 1964. MR 0163376 |
Reference:
|
[6] Y. M. M. Bishop S. E. Fienberg, P. W. Holland: Discrete Multivariate Analysis: Theory and Practice.MIT Press, Cambridge, Mass. 1975. MR 0381130 |
Reference:
|
[7] Ph. Daget, M. Godron: Analyse Fréquentielle de L'Écologie.Masson, Paris 1982. |
Reference:
|
[8] Z. Daróczy: Generalized information functions.Inform, and Control 16 (1970), 36-51. MR 0272528 |
Reference:
|
[9] H. Emptoz: Informations Utiles et Pseudoquestionnaires.Thèse. Universite Claude-Bernard, Lyon 1976. |
Reference:
|
[10] M. A. Gil: A note on stratification and gain in precision in estimating diversity from large samples.Comm. Statist. - Theory Methods 18 (1989), 1521-1526. Zbl 0696.62261, MR 1010120 |
Reference:
|
[11] M. A. Gil: A note on the choice of the sample size in estimating the mutual information.Appl. Math. Comput. 50(1989), 3, 125-132. MR 0986333 |
Reference:
|
[12] M. A. Gil R. Pérez, P. Gil: The mutual information. Estimation in the sampling without replacement.Kybernetika 23 (1987), 5, 406 - 419. MR 0915692 |
Reference:
|
[13] M. A. Gil R. Pérez, I. Martinez: The mutual information.Estimation in the sampling with replacement. RAIRO - Rech. Oper. 20 (1986), 3, 257-268. MR 0872643 |
Reference:
|
[14] 1. J. Good: The population frequencies of species and the estimation of population parameters.Biometrika 40 (1953), 237-264. Zbl 0051.37103, MR 0061330 |
Reference:
|
[15] J. Havrda, F. Charvát: Quantification method of classification processes.Kybernetika 3 (1967), 30-35. MR 0209067 |
Reference:
|
[16] P. Holgate: The statistical entropy of a sample from a community of species.Biometrics 37 (1981), 795-799. Zbl 0506.62094, MR 0675319 |
Reference:
|
[17] Z. K. Lomnicki, S. K. Zaremba: The asymptotic distribution of estimators of the amount of transmitted information.Inform, and Control 2 (1959), 260-284. MR 0109758 |
Reference:
|
[18] J. A. Ludwig, J. F. Reynolds: Statistical Ecology.Wiley Interscience, New York 1988. |
Reference:
|
[19] D. R. Margalef: Information theory in ecology.General Systems 3 (1958), 36 - 71. |
Reference:
|
[20] T. K. Nayak: On diversity measures based on entropy functions.Comm. Statist. - Theory Methods 74(1985), 1, 203-215. Zbl 0561.62004, MR 0788794 |
Reference:
|
[21] G. P. Patil, C Taile: Diversity as a concept and its measurement.J. Amer. Statist. Assoc. 77(1982), 548-567. MR 0675883 |
Reference:
|
[22] E. C Pielou: Ecological Diversity.Wiley Interscience, New York 1975. |
Reference:
|
[23] C R. Rao: Diversity: its measurement, decomposition, apportionment and analysis.Sankhya Ser. A 44 (1982), 1, 1-22. Zbl 0584.62114, MR 0753075 |
Reference:
|
[24] A. Renyi: On measures of entropy and information.Berkeley Symp. Math. Statist, and Prob. 7(1961), 547-561, Univ. California Press, Berkeley, Calif. 196. Zbl 0106.33001, MR 0132570 |
Reference:
|
[25] R. D. Routledge: Diversity indices. Which ones are admissible?.J. Theoret. Biology 76 (1979), 503-515. MR 0527562 |
Reference:
|
[26] C E. Shannon: A mathematical theory of communications.Bell System Technology Journal 27 (1948), 379-423, 623-656. MR 0026286 |
Reference:
|
[27] W. Smith, F. Grassle: Sampling properties of a family of diversity measures.Biometrics 33 (1977), 283-292. Zbl 0357.92026, MR 0488585 |
Reference:
|
[28] K. Zografos K. Ferentinos, T. Papaioannou: $\varphi$-divergence statistics: sampling properties and mutinomial goodness of fit and divergence tests.Comm. Statist. -Theory Methods 19 (1990), 1785-1802. MR 1075502 |
Reference:
|
[29] J. Zvarova: The asymptotic distributions of sample information measure of dependence.Kybernetika 5 (1969), 1, 50-59. MR 0242570 |
Reference:
|
[30] J. Zvarova: On asymptotic behaviour of a sample estimator of Renyi's information of order $\alpha$.In: Trans. Sixth Prague Conf. Inform. Theory, Statist. Dec. Funct., Random Proc, Academia, Prague 1973, pp. 919-924. Zbl 0299.94017, MR 0365800 |
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