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References:
[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. MR 0127457 | Zbl 0092.36701
[2] T. N. Bhargava, P. H. Doyle: A geometric study of diversity. J. Theoret. Biology 43 (1974), 241-251.
[3] T. N. Bhargava, V. R. R. Uppuluri: Sampling distribution of Gini's index of diversity. Appl. Math. Comput. 3 (1977), 1-24. MR 0436416 | Zbl 0403.62018
[4] P. J. Bickel, K. A. Doksum: Mathematical Statistics. Holden-Day, Inc., Oakland 1977. MR 0443141 | Zbl 0403.62001
[5] Z. W. Birnbaum: Introduction to Probability and Mathematical Statistics. Harper & Row, New York 1964. MR 0163376
[6] Y. M. M. Bishop S. E. Fienberg, P. W. Holland: Discrete Multivariate Analysis: Theory and Practice. MIT Press, Cambridge, Mass. 1975. MR 0381130
[7] Ph. Daget, M. Godron: Analyse Fréquentielle de L'Écologie. Masson, Paris 1982.
[8] Z. Daróczy: Generalized information functions. Inform, and Control 16 (1970), 36-51. MR 0272528
[9] H. Emptoz: Informations Utiles et Pseudoquestionnaires. Thèse. Universite Claude-Bernard, Lyon 1976.
[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. MR 1010120 | Zbl 0696.62261
[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
[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
[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
[14] 1. J. Good: The population frequencies of species and the estimation of population parameters. Biometrika 40 (1953), 237-264. MR 0061330 | Zbl 0051.37103
[15] J. Havrda, F. Charvát: Quantification method of classification processes. Kybernetika 3 (1967), 30-35. MR 0209067
[16] P. Holgate: The statistical entropy of a sample from a community of species. Biometrics 37 (1981), 795-799. MR 0675319 | Zbl 0506.62094
[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
[18] J. A. Ludwig, J. F. Reynolds: Statistical Ecology. Wiley Interscience, New York 1988.
[19] D. R. Margalef: Information theory in ecology. General Systems 3 (1958), 36 - 71.
[20] T. K. Nayak: On diversity measures based on entropy functions. Comm. Statist. - Theory Methods 74(1985), 1, 203-215. MR 0788794 | Zbl 0561.62004
[21] G. P. Patil, C Taile: Diversity as a concept and its measurement. J. Amer. Statist. Assoc. 77(1982), 548-567. MR 0675883
[22] E. C Pielou: Ecological Diversity. Wiley Interscience, New York 1975.
[23] C R. Rao: Diversity: its measurement, decomposition, apportionment and analysis. Sankhya Ser. A 44 (1982), 1, 1-22. MR 0753075 | Zbl 0584.62114
[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. MR 0132570 | Zbl 0106.33001
[25] R. D. Routledge: Diversity indices. Which ones are admissible?. J. Theoret. Biology 76 (1979), 503-515. MR 0527562
[26] C E. Shannon: A mathematical theory of communications. Bell System Technology Journal 27 (1948), 379-423, 623-656. MR 0026286
[27] W. Smith, F. Grassle: Sampling properties of a family of diversity measures. Biometrics 33 (1977), 283-292. MR 0488585 | Zbl 0357.92026
[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
[29] J. Zvarova: The asymptotic distributions of sample information measure of dependence. Kybernetika 5 (1969), 1, 50-59. MR 0242570
[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. MR 0365800 | Zbl 0299.94017
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