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Multivariate dynamic information

Author

Listed:
  • Ebrahimi, Nader
  • Kirmani, S.N.U.A.
  • Soofi, Ehsan S.

Abstract

This paper develops measures of information for multivariate distributions when their supports are truncated progressively. The focus is on the joint, marginal, and conditional entropies, and the mutual information for residual life distributions where the support is truncated at the current ages of the components of a system. The current ages of the components induce a joint dynamic into the residual life information measures. Our study of dynamic information measures includes several important bivariate and multivariate lifetime models. We derive entropy expressions for a few models, including Marshall-Olkin bivariate exponential. However, in general, study of the dynamics of residual information measures requires computational techniques or analytical results. A bivariate gamma example illustrates study of dynamic information via numerical integration. The analytical results facilitate studying other distributions. The results are on monotonicity of the residual entropy of a system and on transformations that preserve the monotonicity and the order of entropies between two systems. The results also include a new entropy characterization of the joint distribution of independent exponential random variables.

Suggested Citation

  • Ebrahimi, Nader & Kirmani, S.N.U.A. & Soofi, Ehsan S., 2007. "Multivariate dynamic information," Journal of Multivariate Analysis, Elsevier, vol. 98(2), pages 328-349, February.
    • Handle: RePEc:eee:jmvana:v:98:y:2007:i:2:p:328-349
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    References listed on IDEAS

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    1. Johnson, N. L. & Kotz, Samuel, 1975. "A vector multivariate hazard rate," Journal of Multivariate Analysis, Elsevier, vol. 5(1), pages 53-66, March.
    2. Ebrahimi, Nader & Kirmani, S. N. U. A., 1996. "Some results on ordering of survival functions through uncertainty," Statistics & Probability Letters, Elsevier, vol. 29(2), pages 167-176, August.
    3. Zografos, K., 1999. "On Maximum Entropy Characterization of Pearson's Type II and VII Multivariate Distributions," Journal of Multivariate Analysis, Elsevier, vol. 71(1), pages 67-75, October.
    4. Arnold Zellner, 1997. "Bayesian Analysis in Econometrics and Statistics," Books, Edward Elgar Publishing, number 825.
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    Cited by:

    1. Ebrahimi, Nader & Soofi, Ehsan S. & Soyer, Refik, 2008. "Multivariate maximum entropy identification, transformation, and dependence," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1217-1231, July.
    2. Nair Rohini S. & Abdul Sathar E. I., 2019. "Bivariate Dynamic Weighted Survival Entropy of Order đ›Œ," Stochastics and Quality Control, De Gruyter, vol. 34(2), pages 67-85, December.
    3. Maryam Eskandarzadeh & Antonio Di Crescenzo & Saeid Tahmasebi, 2019. "Cumulative Measure of Inaccuracy and Mutual Information in k -th Lower Record Values," Mathematics, MDPI, vol. 7(2), pages 1-19, February.
    4. Ebrahimi, Nader & Jalali, Nima Y. & Soofi, Ehsan S., 2014. "Comparison, utility, and partition of dependence under absolutely continuous and singular distributions," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 32-50.
    5. Navarro, J. & Sunoj, S.M. & Linu, M.N., 2011. "Characterizations of bivariate models using dynamic Kullback-Leibler discrimination measures," Statistics & Probability Letters, Elsevier, vol. 81(11), pages 1594-1598, November.
    6. Athanasios Sachlas & Takis Papaioannou, 2014. "Residual and Past Entropy in Actuarial Science and Survival Models," Methodology and Computing in Applied Probability, Springer, vol. 16(1), pages 79-99, March.
    7. Antonio Di Crescenzo & Patrizia Di Gironimo, 2018. "Stochastic Comparisons and Dynamic Information of Random Lifetimes in a Replacement Model," Mathematics, MDPI, vol. 6(10), pages 1-13, October.
    8. Amit Ghosh & Chanchal Kundu, 2019. "Bivariate extension of (dynamic) cumulative residual and past inaccuracy measures," Statistical Papers, Springer, vol. 60(6), pages 2225-2252, December.
    9. Amit Ghosh & Chanchal Kundu, 2018. "Chernoff distance for conditionally specified models," Statistical Papers, Springer, vol. 59(3), pages 1061-1083, September.
    10. Nader Ebrahimi & S.N.U.A. Kirmani & Ehsan S. Soofi, 2011. "Predictability of operational processes over finite horizon," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(6), pages 531-545, September.

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