The mutual information estimation in the sampling with replacement
RAIRO - Operations Research - Recherche Opérationnelle, Tome 20 (1986) no. 3, pp. 257-268. 
@article{RO_1986__20_3_257_0,
     author = {Gil, M. A. and Perez, R. and Martinez, I.},
     title = {The mutual information estimation in the sampling with replacement},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {257--268},
     publisher = {EDP-Sciences},
     volume = {20},
     number = {3},
     year = {1986},
     mrnumber = {872643},
     zbl = {0607.62036},
     language = {en},
     url = {http://www.numdam.org/item/RO_1986__20_3_257_0/}
}
TY  - JOUR
AU  - Gil, M. A.
AU  - Perez, R.
AU  - Martinez, I.
TI  - The mutual information estimation in the sampling with replacement
JO  - RAIRO - Operations Research - Recherche Opérationnelle
PY  - 1986
SP  - 257
EP  - 268
VL  - 20
IS  - 3
PB  - EDP-Sciences
UR  - http://www.numdam.org/item/RO_1986__20_3_257_0/
LA  - en
ID  - RO_1986__20_3_257_0
ER  - 
%0 Journal Article
%A Gil, M. A.
%A Perez, R.
%A Martinez, I.
%T The mutual information estimation in the sampling with replacement
%J RAIRO - Operations Research - Recherche Opérationnelle
%D 1986
%P 257-268
%V 20
%N 3
%I EDP-Sciences
%U http://www.numdam.org/item/RO_1986__20_3_257_0/
%G en
%F RO_1986__20_3_257_0
Gil, M. A.; Perez, R.; Martinez, I. The mutual information estimation in the sampling with replacement. RAIRO - Operations Research - Recherche Opérationnelle, Tome 20 (1986) no. 3, pp. 257-268. http://www.numdam.org/item/RO_1986__20_3_257_0/

1. J. Aczel and Z. Daroczy, On Measures of Information and Their Characterizations, Academic Press (New York), 1975. | MR | Zbl

2. J. Aczel and Pl. Kannapan, A Mixed Theory of Information. III. Inset Entropies of Degree ß, Inf. and Contr., 39, 1978, 315-322. | MR | Zbl

3. N. L. Aggarwal, Y. Cesari and C. F. Picard, Propriétés de branchement liées aux questionnaires de Campbell et à l'information de Renyi, C.R. Acad. Sc. Paris, Série A, t.275, 437-440, 1972. | MR | Zbl

4. F. Azorin, Curso de Muestreo y Applicaciones, Ed. Aguilar (Madrid), 1972.

5. F. Azorin, Diversity and Uncertainty, Proc. F.I.S.A.L.-83 (Palma de Mallorca), 1983, 37-44.

6. T. N. Bhargava and V. R. R. Uppuluri, On an axiomatic derivation of Gini diversity with applications, Metron, Vol. XXXIII, N.l-2, 1985. | MR | Zbl

7. T. N. Bhargava and V. R. R. Uppuluri, Sampling Distribution of Gini's index of diversity, Appl. Math. Comput., 3, 1-24, 1977. | MR | Zbl

8. F. Bourguignon, Decomposable income inequality measures, Econometrica, 47, 901-920, 1979. | MR | Zbl

9. W. G. Cochran, Sampling Techniques, John Wiley (New York), 1967. | Zbl

10. F. A. Cowell, On the structure of additive inequality measures, Review of Economic Studies, 47, 521-531, 1980. | Zbl

11. Z. Daroczy, Generalized Information Functions, Inf. and Contr., 16, 36-51, 1970. | MR | Zbl

12. W. Eichhorn and W. Gehrig, Measurement of Inequality in Economics, Modern Applied Mathematics Optimization and Operations Research, Ed. B. Korte, North Holland (Amsterdam), 1982. | Zbl

13. H. Emptoz, Informations utiles et pseudoquestionnaires, These, Université Claude-Bernard (Lyon), 1976.

14. M. A. Gil, Estudio de una medida para la incertidumbre correspondiente a las utilidades, Trab. de Est. e Inv. Oper., Vol. 32, 3, 45-66, 1981.

15. M. A Gil, Criterion of Maximizing the Expected Quietness (invariant by homotheties in relation to the utilities), R.A.Ï.R.O.-Rech. Opér., 16, 319-331, 1982. | Numdam | MR | Zbl

16. M. A. Gil, Mixed Criterion of Expected Utility and Quietness (invariant by homotheties with respect to the utilities), Statistica, Anno XLII, n.l, 21-37, 1982. | MR | Zbl

17. P. Gil Teoria Matemática de la Información, Ed. ICE (Madrid), 1981.

18. J. Havrda and F. Charvat, Quantification method of classification processes, Kybernetica, 3, 30-35, 1967. | MR | Zbl

19. Sir M. Kendall and A. Stuart, The Advanced Theory of Statistics, Charles Griffin Co. Ltd. (London), 1977-83. | Zbl

20. A. M. Mathai and P. N. Rathie, Basic Concepts in Information Theory and Statistics, Wiley Eastern Limited (New Delhi), 1975. | MR | Zbl

21. O. Onicescu, Energie Informationnelle, C. R. Acad. Sci. Paris, Série A, t. 263, 1966, 841-842. | MR | Zbl

22. R. Perez, Estimación de la incertidumbre, la incertidumbre ùtil y la inquietud en poblaciones finitas. Una aplicación a las medidas de desigualdad, Sesión Científica de la Real Acad. Ciencias de Madrid, 10 Abril, 1985.

23. R. Perez, M. A. Gil and P. Gil, Estimating the Uncertainly associated with a Variable in a Finite Population, Kybernetes, 15 (3), 1986. | MR | Zbl

24. C. F. Picard, Graphes et Questionnaires, Tome 2, Gauthier-Villars Ed. (Paris), 1972. | Zbl

25. E. C. Pielou, An Introduction to Mathematical Diversity, Wiley-Interscience (New York), 1969. | Zbl

26. P. N. Rathie and Pl. Kannappan, An inaccuracy function of the type ß, Ann. Inst. Statist. Math., 25, 205-214, 1973. | MR | Zbl

27. C. E. Shannon, A Mathematical Theory of Communication, Bell. System. Tech., J. 27, 379-423, 1948. | MR | Zbl

28. A. F. Shorrocks, The class of additively decomposable inequality measures, Econometrica, 48, 613-625, 1980. | MR | Zbl

29. E. H. Simpson, Measurement of Diversity, Nature, 163, 688, 1949. | Zbl

30. H. Theil, Economics and Information Theory, North Holland (Amsterdam), 1967.

31. D. Zagier, On the decomposability of the Gini coefficient and other indices of inequality. Discussion Paper No. 108, Projectgruppe Theoretische Modelle, Universität Bonn, 1983.