Some results concerning maximum Rényi entropy distributions

Oliver Johnson; Christophe Vignat

Annales de l'I.H.P. Probabilités et statistiques (2007)

  • Volume: 43, Issue: 3, page 339-351
  • ISSN: 0246-0203

How to cite

top

Johnson, Oliver, and Vignat, Christophe. "Some results concerning maximum Rényi entropy distributions." Annales de l'I.H.P. Probabilités et statistiques 43.3 (2007): 339-351. <http://eudml.org/doc/77937>.

@article{Johnson2007,
author = {Johnson, Oliver, Vignat, Christophe},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {entropy power inequality; Fisher information; heat equation; maximum entropy; Rényi entropy},
language = {eng},
number = {3},
pages = {339-351},
publisher = {Elsevier},
title = {Some results concerning maximum Rényi entropy distributions},
url = {http://eudml.org/doc/77937},
volume = {43},
year = {2007},
}

TY - JOUR
AU - Johnson, Oliver
AU - Vignat, Christophe
TI - Some results concerning maximum Rényi entropy distributions
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2007
PB - Elsevier
VL - 43
IS - 3
SP - 339
EP - 351
LA - eng
KW - entropy power inequality; Fisher information; heat equation; maximum entropy; Rényi entropy
UR - http://eudml.org/doc/77937
ER -

References

top
  1. [1] S.M. Ali, S.D. Silvey, A general class of coefficients of divergence of one distribution from another, J. Roy. Statist. Soc. Ser. B28 (1966) 131-142. Zbl0203.19902MR196777
  2. [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. Zbl1036.52004MR2083383
  3. [3] N.M. Blachman, The convolution inequality for entropy powers, IEEE Trans. Inform. Theory11 (1965) 267-271. Zbl0134.37401MR188004
  4. [4] A. Compte, D. Jou, Non-equilibrium thermodynamics and anomalous diffusion, J. Phys. A29 (15) (1996) 4321-4329. Zbl0900.82066MR1413205
  5. [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. [6] T.M. Cover, J.A. Thomas, Elements of Information Theory, John Wiley, New York, 1991. Zbl0762.94001MR1122806
  7. [7] I. Csiszár, Information-type measures of difference of probability distributions and indirect observations, Studia Sci. Math. Hungar.2 (1967) 299-318. Zbl0157.25802MR219345
  8. [8] A. Dembo, T.M. Cover, J.A. Thomas, Information theoretic inequalities, IEEE Trans. Inform. Theory37 (6) (1991) 1501-1518. Zbl0741.94001MR1134291
  9. [9] C.W. Dunnett, M. Sobel, A bivariate generalization of Student's t-distribution, with tables for certain special cases, Biometrika41 (1954) 153-169. Zbl0056.36703MR61793
  10. [10] M.L. Eaton, On the projections of isotropic distributions, Ann. Statist.9 (2) (1981) 391-400. Zbl0463.62016MR606622
  11. [11] R.A. Fisher, Frequency distribution of the values of the correlation coefficient in samples from an indefinitely large population, Biometrika10 (1915) 507-521. 
  12. [12] B.V. Gnedenko, V.Y. Korolev, Random Summation: Limit Theorems and Applications, CRC Press, Boca Raton, FL, 1996. Zbl0857.60002MR1387113
  13. [13] O.T. Johnson, Y.M. Suhov, Entropy and random vectors, J. Statist. Phys.104 (1) (2001) 147-167. Zbl0987.60034MR1851387
  14. [14] S. Kullback, R. Leibler, On information and sufficiency, Ann. Math. Statist.22 (1951) 79-86. Zbl0042.38403MR39968
  15. [15] E. Lutwak, D. Yang, G. Zhang, Moment-entropy inequalities, Ann. Probab.32 (1B) (2004) 757-774. Zbl1053.60004MR2039942
  16. [16] E. Lutwak, D. Yang, G. Zhang, Cramer–Rao and moment-entropy inequalities for Rényi entropy and generalized Fisher information, IEEE Trans. Inform. Theory51 (2005) 473-478. Zbl1205.94059
  17. [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. Zbl0106.33001MR132570
  18. [18] C.E. Shannon, W.W. Weaver, A Mathematical Theory of Communication, University of Illinois Press, Urbana, IL, 1949. Zbl0041.25804MR32134

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.