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Dynamic generalized information measures


  • Asadi, Majid
  • Ebrahimi, Nader
  • Soofi, Ehsan S.


In many reliability and survival analysis problems the current age of an item under study must be taken into account by information measures of the lifetime distribution. Kullback-Leibler information and Shannon entropy have been considered in this context, which led to information measures that depend on time, and thus are dynamic. This paper develops dynamic information divergence and entropy of order [alpha], also known as Rényi information and entropy, which for [alpha]=1 give the Kullback-Leibler information and Shannon entropy, respectively. We give characterizations of the proportional hazards model, the exponential distribution, and Generalized Pareto distributions in terms of dynamic Rényi information and entropy. It is also shown that dynamic Rényi entropy uniquely determines distributions that have monotone densities. A result that relates dynamic Rényi entropy and hazard rate orderings is given. This result leads to a Maximum Dynamic Entropy of order [alpha] formulation and characterizations of some well-known lifetime models. A dynamic entropy hazard rate inequality is developed as an analog of the well-known entropy moment inequality.

Suggested Citation

  • Asadi, Majid & Ebrahimi, Nader & Soofi, Ehsan S., 2005. "Dynamic generalized information measures," Statistics & Probability Letters, Elsevier, vol. 71(1), pages 85-98, January.
  • Handle: RePEc:eee:stapro:v:71:y:2005:i:1:p:85-98

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    References listed on IDEAS

    1. Golan, Amos & Perloff, Jeffrey M., 2002. "Comparison of maximum entropy and higher-order entropy estimators," Journal of Econometrics, Elsevier, vol. 107(1-2), pages 195-211, March.
    2. Di Crescenzo, Antonio & Longobardi, Maria, 2004. "A measure of discrimination between past lifetime distributions," Statistics & Probability Letters, Elsevier, vol. 67(2), pages 173-182, April.
    3. Felix Belzunce & Jorge Navarro & José M. Ruiz & Yolanda del Aguila, 2004. "Some results on residual entropy function," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 59(2), pages 147-161, May.
    4. Zografos, K. & Nadarajah, S., 2005. "Expressions for Rényi and Shannon entropies for multivariate distributions," Statistics & Probability Letters, Elsevier, vol. 71(1), pages 71-84, January.
    5. Nader Ebrahimi & S. Kirmani, 1996. "A measure of discrimination between two residual life-time distributions and its applications," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 48(2), pages 257-265, June.
    6. Asadi, Majid & Ebrahimi, Nader, 2000. "Residual entropy and its characterizations in terms of hazard function and mean residual life function," Statistics & Probability Letters, Elsevier, vol. 49(3), pages 263-269, September.
    7. 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.
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    Cited by:

    1. Abbasnejad, M. & Arghami, N.R. & Morgenthaler, S. & Mohtashami Borzadaran, G.R., 2010. "On the dynamic survival entropy," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1962-1971, December.
    2. Kayal, Suchandan, 2015. "On generalized dynamic survival and failure entropies of order (α,β)," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 123-132.
    3. Nanda, Asok K. & Sankaran, P.G. & Sunoj, S.M., 2014. "Rényi’s residual entropy: A quantile approach," Statistics & Probability Letters, Elsevier, vol. 85(C), pages 114-121.
    4. K. Nair & P. Sankaran & S. Smitha, 2011. "Chernoff distance for truncated distributions," Statistical Papers, Springer, vol. 52(4), pages 893-909, November.


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