New copulas obtained by maximizing Tsallis or Rényi entropies

AIP Conference Proceedings

Volumn 1443, Issue , 2012, Pages 238-249

  Pougaza, Doriano Boris ^a   Mohammad Djafari, Ali ^a  

^a UNIV PARIS SUD   (France)

Author keywords

Copula; Entropy; Joint density estimation; R nyi and Tsallis; Shannon

Indexed keywords

EID: 84861114768     PISSN: 0094243X     EISSN: 15517616     Source Type: Conference Proceeding    
DOI: 10.1063/1.3703641     Document Type: Conference Paper

References (25)

1. A. Sklar. Fonctions de répartition à n dimensions et leurs marges. Publ. Inst. Statist. Univ. Paris 8, pages 229-231, 1959.
2. M. Fréchet. Sur les tableaux de corrélation dont les marges sont données. Ann. Univ. Lyon, III. Sér., Sect. A, 14:53-77, 1951.
3. C.E. Shannon. A mathematical theory of communication. Bell System Technical Journal, 27:432-379, 1948.
4. J. Havrda and F. Charvát. Quantificationmethod of classification processes. Kybernetika, 3(1):30-35, 1967.
5. C. Tsallis. Possible generalization of Boltzmann-Gibbs statistics. Journal of statistical physics, 52(1):479-487, 1988.
6. A. Rényi. On measures of dependence. Acta Mathematica Hungarica, 10(3):441-451, 1959.
7. A. Markoe. Analytic Tomography. Cambridge University Press, 2006.
8. G. Dall'Aglio, S. Kotz, and G. Salinetti. Advances in probability distributions with given marginals: beyond the copulas. Kluwer Academic Publ., Dordrecht, 1991.
9. C. Genest and L.P. Rivest. Statistical inference procedures for bivariate archimedean copulas. Journal of the American Statistical Association, 88(423):1034-1043, 1993.
10. H. Joe. Multivariate Models and Dependence Concepts. London: Chapman & Hall, 1997.
11. Roger B. Nelsen. An Introduction to Copulas. Springer Verlag, 2nd edition, 2006.
12. A.M.H.Meeuwissen and T. Bedford. Minimally informative distributions with given rank correlation for use in uncertainty analysis. Journal of Statistical Computation and Simulation, 57(1):143-174, 1997.
13. E. Pasha and S.Mansoury. Determination ofMaximumEntropyMultivariate ProbabilityDistribution under some Constraints. Applied Mathematical Sciences, 2(57):2843-2849, 2008.
14. J. Piantadosi, P. Howlett, and J. Borwein. Copulas with Maximum Entropy. Optimization Letters, 5:1-27, 2011.
15. L. Rüschendorf. Construction of multivariate distributions with given marginals. Annals of the Institute of Statistical Mathematics, 37(1):225-233, 1985.
16. C.D. Lai and M. Xie. A new family of positive quadrant dependent bivariate distributions. Statistics & probability letters, 46(4):359-364, 2000.
17. D.-B. Pougaza and A. Mohammad-Djafari. Maximum entropies copulas. In Proceedings of the 30th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, volume 1305, pages 329-336. American Institute of Physics, 2011.
18. Roger B. Nelsen. Concordance and copulas: A survey. Distributions with given marginals and statistical modelling, pages 169-178, 2002.
19. F. Schmid, R. Schmidt, T. Blumentritt, S. Gaißer, and M. Ruppert. Copula-based measures of multivariate association. In Copula Theory and Its Applications: Proceedings of the Workshop Held in Warsaw, 25-26 September 2009, volume 198, page 209. Springer Verlag, 2010.
20. A.W. Marshall and I. Olkin. Life distributions: Structure of nonparametric, semiparametric, and parametric families. Springer Verlag, 2007.
21. J.A. Rodríguez-Lallena and M. Úbeda-Flores. A new class of bivariate copulas. Statistics & probability letters, 66(3):315-325, 2004.
22. G. A. Fredricks and Roger B. Nelsen. On the relationship between spearman's rho and kendall's tau for pairs of continuous random variables. Journal of Statistical Planning and Inference, 137:2143-2150, 2007.
23. P. Kumaraswamy. A generalized probability density function for double-bounded random processes. Journal of Hydrology, 46(1-2):79-88, 1980.
24. M.C. Jones. Kumaraswamy's distribution:A beta-type distributionwith some tractability advantages. Statistical Methodology, 6(1):70-81, 2009.
25. J.R. Van Dorp and S. Kotz. The Standard Two-Sided Power Distribution and its Properties. The American Statistician, 56(2):90-99, 2002.