Journal of Applied Probability

Minimum dynamic discrimination information models

Majid Asadi, Nader Ebrahimi, G. G. Hamedani, and Ehsan S. Soofi

Full-text: Access has been disabled (more information)

Abstract

In this paper, we introduce the minimum dynamic discrimination information (MDDI) approach to probability modeling. The MDDI model relative to a given distribution G is that which has least Kullback-Leibler information discrepancy relative to G, among all distributions satisfying some information constraints given in terms of residual moment inequalities, residual moment growth inequalities, or hazard rate growth inequalities. Our results lead to MDDI characterizations of many well-known lifetime models and to the development of some new models. Dynamic information constraints that characterize these models are tabulated. A result for characterizing distributions based on dynamic Rényi information divergence is also given.

Article information

Source
J. Appl. Probab. Volume 42, Number 3 (2005), 643-660.

Dates
First available in Project Euclid: 21 September 2005

Permanent link to this document
http://projecteuclid.org/euclid.jap/1127322018

Digital Object Identifier
doi:10.1239/jap/1127322018

Mathematical Reviews number (MathSciNet)
MR2157511

Zentralblatt MATH identifier
1094.94013

Subjects
Primary: 94A15: Information theory, general [See also 62B10, 81P94]
Secondary: 60E15: Inequalities; stochastic orderings 60B05: Probability measures on topological spaces

Keywords
Lifetime distribution residual life distribution monotone density failure rate dominance uncertainty ordering

Citation

Asadi, Majid; Ebrahimi, Nader; Hamedani, G. G.; Soofi, Ehsan S. Minimum dynamic discrimination information models. J. Appl. Probab. 42 (2005), no. 3, 643--660. doi:10.1239/jap/1127322018. http://projecteuclid.org/euclid.jap/1127322018.


Export citation

References

  • Asadi, M., Ebrahimi, N., Hamedani, G. G. and Soofi, E. S. (2004). Maximum dynamic entropy models. J. Appl. Prob. 41, 379--390.
    Mathematical Reviews (MathSciNet): MR2052579
    Digital Object Identifier: doi:10.1239/jap/1082999073
    Zentralblatt MATH: 1063.94015
  • Belzunce, F., Navarro, J., Ruiz, J. M. and del Aguila, Y. (2004). Some results on residual entropy functions. Metrika 59, 147--161.
    Mathematical Reviews (MathSciNet): MR2059033
    Digital Object Identifier: doi:10.1007/s001840300276
    Zentralblatt MATH: 1079.62008
  • Di Crescenzo, A. and Longobardi, M. (2002). Entropy-based measure of uncertainty in past lifetime distributions. J. Appl. Prob. 39, 434--440.
    Mathematical Reviews (MathSciNet): MR1908960
    Digital Object Identifier: doi:10.1239/jap/1025131441
    Zentralblatt MATH: 1003.62087
  • Ebrahimi, N. (1996). How to measure uncertainty in the residual lifetime distributions. Sankhyā A 58, 48--57.
    Mathematical Reviews (MathSciNet): MR1659063
  • Ebrahimi, N. (1998). Testing for exponentiality of the residual lifetime based on dynamic Kullback--Leibler information. IEEE Trans. Reliab. 47, 197--201.
  • Ebrahimi, N. (2001). Testing for uniformity of the residual lifetime based on dynamic Kullback--Leibler information. Ann. Inst. Statist. Math. 53, 325--337.
    Mathematical Reviews (MathSciNet): MR1841139
    Digital Object Identifier: doi:10.1023/A:1012085320762
    Zentralblatt MATH: 1027.62025
  • Ebrahimi, N. and Kirmani, S. N. U. A. (1996a). A characterization of the proportional hazards model through a measure of discrimination between two residual life distributions. Biometrika 83, 233--235.
    Mathematical Reviews (MathSciNet): MR1399168
    Zentralblatt MATH: 0865.62075
    Digital Object Identifier: doi:10.1093/biomet/83.1.233
  • Ebrahimi, N. and Kirmani, S. N. U. A. (1996b). Some results on ordering of survival functions through uncertainty. Statist. Prob. Lett. 29, 167--176.
    Mathematical Reviews (MathSciNet): MR1411415
  • Hamedani, G. G. (2005). Characterizations of univariate continuous distributions based on hazard functions. To appear in J. Appl. Statist. Sci.
    Mathematical Reviews (MathSciNet): MR2116955
  • Jaynes, E. T. (1957). Information theory and statistical mechanics. Physics Rev. 106, 620--630.
    Mathematical Reviews (MathSciNet): MR87305
    Digital Object Identifier: doi:10.1103/PhysRev.106.620
  • Jaynes, E. T. (1982). On the rationale of maximum entropy methods. Proc. IEEE 70, 939--952.
  • Kullback, S. (1959). Information Theory and Statistics. John Wiley, New York.
    Mathematical Reviews (MathSciNet): MR103557
    Zentralblatt MATH: 0088.10406
  • Rényi, A. (1961). On measures of entropy and information. In Proc. 4th Berkeley Symp. Math. Statist. Prob., Vol. 1, University of California Press, Berkeley, CA, pp. 547--561.
    Mathematical Reviews (MathSciNet): MR132570
  • Shaked, M. and Shanthikumar, J. G. (1994). Stochastic Orders and Their Applications. Academic Press, Boston, MA.
    Mathematical Reviews (MathSciNet): MR1278322
    Zentralblatt MATH: 0806.62009
  • Shannon, C. E. (1948). A mathematical theory of communication. Bell System Tech. J. 27, 379--423, 623--656.
    Mathematical Reviews (MathSciNet): MR26286
  • Shore, J. E. and Johnson, R. W. (1980). Axiomatic derivation of the principle of maximum entropy and principle of minimum cross-entropy. IEEE Trans. Inf. Theory 26, 26--37.
    Mathematical Reviews (MathSciNet): MR560389
    Digital Object Identifier: doi:10.1109/TIT.1980.1056144

Applied Probability Trust

Journal of Applied Probability

New content alerts

Email RSS ToC RSS Article
  • You have access to this content.
  • You have partial access to this content.
  • You do not have access to this content.
Turn Off MathJax

What is MathJax?

More like this

+ See more