Multivariate dynamic information

Journal of Multivariate Analysis

Volumn 98, Issue 2, 2007, Pages 328-349

  Ebrahimi, Nader ^a   Kirmani, S N U A ^b   Soofi, Ehsan S ^c  

^a NORTHERN ILLINOIS UNIVERSITY   (United States)

^b UNIVERSITY OF NORTHERN IOWA   (United States)

^c UNIVERSITY OF WISCONSIN MILWAUKEE   (United States)

Author keywords

Entropy; Independence; Kullback Leibler information; Mutual information; Reliability; Residual life

Indexed keywords

EID: 33750494158     PISSN: 0047259X     EISSN: 10957243     Source Type: Journal    
DOI: 10.1016/j.jmva.2005.08.004     Document Type: Article

References (35)

1. Ahsanullah M., and Habibullah M. On the entropies and mutual information of some bivariate continuous distributions used in reliability theory. In: Jewell N.P., Kimber A.C., Lee M.L.T., and Whitemore G.A. (Eds). Lifetime Data: Models in Reliability and Survival Analysis (1996), Kluwer Academic Publishers, Dordrecht 1-5
2. Anderson J.E., Louis T.A., Holm N.V., and Harvald B. Time-dependent association measures for bivariate survival distributions. J. Amer. Statist. Assoc. 87 (1992) 641-650
3. B.C. Arnold, Pareto Distributions, International Co-operative Publication House, Fairland, MD, 1983.
4. Arnold B.C., and Strauss D. Bivariate distribution with exponential conditionals. J. Amer. Statist. Assoc. 83 (1988) 522-527
5. Asadi M., Ebrahimi N., Hamedani G.G., and Soofi E.S. Maximum dynamic entropy models. J. Appl. Probab. 41 (2004) 379-390
6. Barlow R.E., and Proschan F. Statistical Theory of Reliability and Life Testing: Probability Models to Begin With (1981), Silver Spring, MD
7. F. Belzunce, J. Navarro, J. M. Ruiz, Some results on residual entropy functions, Metrika (2004) 147-161.
8. Block H.B., and Basu A.P. A continuous bivariate exponential extension. J. Amer. Statist. Assoc. 69 (1974) 1031-1037
9. Darbellay G.A. An estimator of the mutual information based on a criterion for independence. Comput. Statist. Data Anal. 32 (2000) 1-17
10. Darbellay G.A., and Vajda I. Entropy expressions for multivariate continuous distributions. IEEE Trans. Inform. Theory, IT 46 (2000) 709-712
11. Di Crescenzo A., and Longobardi M. Entropy-based measure of uncertainty in past lifetime distributions. J. Appl. Probab. 39 (2002) 434-440
12. Di Crescenzo A., and Longobardi M. A measure of discrimination between past life-time distributions. Statist. Probab. Lett. 67 (2004) 173-182
13. Ebrahimi N. How to measure uncertainty in the residual lifetime distributions. Sankhya A 58 (1996) 48-57
14. Ebrahimi N. Testing for exponentiality of the residual lifetime based on dynamic Kullback-Leibler information. IEEE Trans. Reliability R-47 (1998) 197-201
15. Ebrahimi N. Testing for uniformity of the residual lifetime based on dynamic Kullback-Leibler information. Ann. Inst. Statist. Math. 53 (2001) 325-337
16. Ebrahimi N., and Ghosh M. Multivariate negative dependence. Comm. Statist. A10 (1981) 307-337
17. Ebrahimi N., and Kirmani S.N.U.A. A characterization of the proportional hazards model through a measure of discrimination between two residual life distributions. Biometrika 83 (1996) 233-235
18. Ebrahimi N., and Kirmani S.N.U.A. Some results on ordering of survival functions through uncertainty. Statist. Probab. Lett. 29 (1996) 167-176
19. N. Ebrahimi, S.N.U.A. Kirmani, E.S. Soofi, Multivariate Sample and Bayesian dynamic information measures, Technical Report, 2005.
20. Ebrahimi N., and Soofi E.S. Information measures for reliability. In: Soyer R., Mazzuchi T.A., and Singpurwalla N.D. (Eds). Mathematical Reliability: An Expository Perspective (2004), Kluwer, The Netherlands 127-159
21. Giovagnoli A., and Wynn H.P. Multivariate dispersion ordering. Statist. Probab. Lett. 22 (1995) 325-332
22. Gumbel E.G. Bivariate exponential distributions. J. Amer. Statist. Assoc. 55 (1960) 698-707
23. Harris R. A multivariate definition for increasing hazard rate distributions. Ann. Inst. Statist. Math. 41 (1970) 713-717
24. Johnson N.L., and Kotz S. A vector multivariate hazard rate. J. Multivariate Anal. 5 (1975) 53-66
25. S. Kotz, N. Balakrishnan, N.L. Johnson, Continuous Multivariate Distributions, vol. 1: Models and Applications, second ed., Wiley, New York, 2000.
26. Kraskov A., Stögbauer H., and Grassberger P. Estimating mutual information. Phys. Rev. E 69 (2004) 066138
27. Kullback S. Information Theory and Statistics (1959), Wiley, New York (reprinted in 1968 by Dover)
28. Lindley D.V. On a measure of information provided by an experiment. Ann. Math. Statist. 27 (1956) 986-1005
29. Marshall A.W., and Olkin I. A multivariate exponential distribution. J. Amer. Statist. Assoc. 62 (1967) 30-44
30. McKay A.T. Sampling from batches. J. Roy. Statist. Soc., Suppl. 1 (1934) 207-216
31. Shaked M., and Shanthikumar J.G. Stochastic Orders and Their Applications (1994), Academic press, New York
32. Singpurwalla N.D. Entropy and information in reliability. In: Berry D., Chaloner K., and Geweke J. (Eds). Bayesian Analysis of Statistics and Econometrics (1997), Wiley, New York
33. Soofi E.S. Capturing the intangible concept of information. J. Amer. Statist. Assoc. 89 (1994) 1243-1254
34. Zellner A. Bayesian Analysis in Econometrics and Statistics: The Zellner View and Papers (1997), Edward Elgar, Cheltenham UK & Lyme, US
35. Zografos K. On maximum entropy characterization of Pearson's Type II and VII multivariate distributions. J. Multivariate Anal. 71 (1999) 67-75