Some results concerning maximum Rényi entropy distributions
Johnson, Oliver ; Vignat, Christophe
Annales de l'I.H.P. Probabilités et statistiques, Tome 43 (2007), p. 339-351 / Harvested from Numdam
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@article{AIHPB_2007__43_3_339_0,
     author = {Johnson, Oliver and Vignat, Christophe},
     title = {Some results concerning maximum R\'enyi entropy distributions},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {43},
     year = {2007},
     pages = {339-351},
     doi = {10.1016/j.anihpb.2006.05.001},
     mrnumber = {2319701},
     zbl = {1135.94317},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_2007__43_3_339_0}
}

Johnson, Oliver; Vignat, Christophe. Some results concerning maximum Rényi entropy distributions. Annales de l'I.H.P. Probabilités et statistiques, Tome 43 (2007) pp. 339-351. doi : 10.1016/j.anihpb.2006.05.001. http://gdmltest.u-ga.fr/item/AIHPB_2007__43_3_339_0/

[1] S.M. Ali, S.D. Silvey, A general class of coefficients of divergence of one distribution from another, J. Roy. Statist. Soc. Ser. B 28 (1966) 131-142. | MR 196777 | Zbl 0203.19902

[2] F. Barthe, M. Csörnyei, A. Naor, A note on simultaneous polar and Cartesian decomposition, in: Geometric Aspects of Functional Analysis, Lecture Notes in Math., vol. 1807, Springer, Berlin, 2003, pp. 1-19. | MR 2083383 | Zbl 1036.52004

[3] N.M. Blachman, The convolution inequality for entropy powers, IEEE Trans. Inform. Theory 11 (1965) 267-271. | MR 188004 | Zbl 0134.37401

[4] A. Compte, D. Jou, Non-equilibrium thermodynamics and anomalous diffusion, J. Phys. A 29 (15) (1996) 4321-4329. | MR 1413205 | Zbl 0900.82066

[5] J. Costa, A. Hero, C. Vignat, On solutions to multivariate maximum α-entropy problems, in: Rangarajan A., Figueiredo M., Zerubia J. (Eds.), EMMCVPR 2003, Lisbon, 7-9 July 2003, Lecture Notes in Computer Science, vol. 2683, Springer-Verlag, Berlin, 2003, pp. 211-228.

[6] T.M. Cover, J.A. Thomas, Elements of Information Theory, John Wiley, New York, 1991. | MR 1122806 | Zbl 0762.94001

[7] I. Csiszár, Information-type measures of difference of probability distributions and indirect observations, Studia Sci. Math. Hungar. 2 (1967) 299-318. | MR 219345 | Zbl 0157.25802

[8] A. Dembo, T.M. Cover, J.A. Thomas, Information theoretic inequalities, IEEE Trans. Inform. Theory 37 (6) (1991) 1501-1518. | MR 1134291 | Zbl 0741.94001

[9] C.W. Dunnett, M. Sobel, A bivariate generalization of Student's t-distribution, with tables for certain special cases, Biometrika 41 (1954) 153-169. | MR 61793 | Zbl 0056.36703

[10] M.L. Eaton, On the projections of isotropic distributions, Ann. Statist. 9 (2) (1981) 391-400. | MR 606622 | Zbl 0463.62016

[11] R.A. Fisher, Frequency distribution of the values of the correlation coefficient in samples from an indefinitely large population, Biometrika 10 (1915) 507-521.

[12] B.V. Gnedenko, V.Y. Korolev, Random Summation: Limit Theorems and Applications, CRC Press, Boca Raton, FL, 1996. | MR 1387113 | Zbl 0857.60002

[13] O.T. Johnson, Y.M. Suhov, Entropy and random vectors, J. Statist. Phys. 104 (1) (2001) 147-167. | MR 1851387 | Zbl 0987.60034

[14] S. Kullback, R. Leibler, On information and sufficiency, Ann. Math. Statist. 22 (1951) 79-86. | MR 39968 | Zbl 0042.38403

[15] E. Lutwak, D. Yang, G. Zhang, Moment-entropy inequalities, Ann. Probab. 32 (1B) (2004) 757-774. | MR 2039942 | Zbl 1053.60004

[16] E. Lutwak, D. Yang, G. Zhang, Cramer-Rao and moment-entropy inequalities for Rényi entropy and generalized Fisher information, IEEE Trans. Inform. Theory 51 (2005) 473-478.

[17] A. Rényi, On measures of entropy and information, in: Neyman J. (Ed.), Proceedings of the 4th Berkeley Conference on Mathematical Statistics and Probability, University of California Press, Berkeley, 1961, pp. 547-561. | MR 132570 | Zbl 0106.33001

[18] C.E. Shannon, W.W. Weaver, A Mathematical Theory of Communication, University of Illinois Press, Urbana, IL, 1949. | MR 32134 | Zbl 0041.25804