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Optimal hazard models based on partial information

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

Abstract

The proportional hazards (PH), mixture hazards (MH), proportional reversed hazards (PRH), and mixture reversed hazards (MRH) models are widely used in various applications in many fields, but their optimality properties remain unknown. We represent these important reliability models as general escort models and derive them as solutions to several information theoretic formulations. Thus far, the escort models are defined in physics by the normalized powers of one or product of two probability mass or density functions and have been derived in statistics and physics as the solutions to different information formulations. The general escort models introduced in this paper include the escorts of densities, as well as the escorts of survival functions and cumulative distribution functions which represent the hazards models. Moreover, we show that the MH and MRH models are also optimal according to formulations in terms of the mean variation distance. Additional results explore reliability properties of the escort of two densities. A notable property is that the escort of two densities with non-constant hazard rates can be a constant hazard rate model. Another result characterizes the PH model in terms of the survival function of the escort of two densities. Comparisons of the MH, escort of two densities, and the mixture of two distributions are illustrated.

Suggested Citation

  • Asadi, Majid & Ebrahimi, Nader & Soofi, Ehsan S., 2018. "Optimal hazard models based on partial information," European Journal of Operational Research, Elsevier, vol. 270(2), pages 723-733.
    • Handle: RePEc:eee:ejores:v:270:y:2018:i:2:p:723-733
    DOI: 10.1016/j.ejor.2018.04.006
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    References listed on IDEAS

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    1. Crescenzo, Antonio Di, 2000. "Some results on the proportional reversed hazards model," Statistics & Probability Letters, Elsevier, vol. 50(4), pages 313-321, December.
    2. Alwan, Layth C. & Ebrahimi, Nader & Soofi, Ehsan S., 1998. "Information theoretic framework for process control," European Journal of Operational Research, Elsevier, vol. 111(3), pages 526-542, December.
    3. Ibrahim J.G. & Chen M-H. & Sinha D., 2003. "On Optimality Properties of the Power Prior," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 204-213, January.
    4. Andersson, Jonas & Jörnsten, Kurt & Nonås, Sigrid Lise & Sandal, Leif & Ubøe, Jan, 2013. "A maximum entropy approach to the newsvendor problem with partial information," European Journal of Operational Research, Elsevier, vol. 228(1), pages 190-200.
    5. Maxim Finkelstein, 2009. "Understanding the shape of the mixture failure rate (with engineering and demographic applications)," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(6), pages 643-663, November.
    6. Maxim S. Finkelstein, 2009. "Understanding the shape of the mixture failure rate (with engineering and demographic applications)," MPIDR Working Papers WP-2009-031, Max Planck Institute for Demographic Research, Rostock, Germany.
    7. Fleischhacker, Adam J. & Fok, Pak-Wing, 2015. "On the relationship between entropy, demand uncertainty, and expected loss," European Journal of Operational Research, Elsevier, vol. 245(2), pages 623-628.
    8. Li, Xiaohu & Da, Gaofeng & Zhao, Peng, 2010. "On reversed hazard rate in general mixture models," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 654-661, April.
    9. Majid Asadi & Nader Ebrahimi & Ehsan S. Soofi & Somayeh Zarezadeh, 2014. "New maximum entropy methods for modeling lifetime distributions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(6), pages 427-434, September.
    10. Francisco J. Samaniego, 2007. "System Signatures and their Applications in Engineering Reliability," International Series in Operations Research and Management Science, Springer, number 978-0-387-71797-5, January.
    11. Li, Xiaohu & Da, Gaofeng, 2010. "Stochastic comparisons in multivariate mixed model of proportional reversed hazard rate with applications," Journal of Multivariate Analysis, Elsevier, vol. 101(4), pages 1016-1025, April.
    12. Park, Sangun & Rao, Murali & Shin, Dong Wan, 2012. "On cumulative residual Kullback–Leibler information," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 2025-2032.
    13. Aktekin, Tevfik, 2014. "Call center service process analysis: Bayesian parametric and semi-parametric mixture modeling," European Journal of Operational Research, Elsevier, vol. 234(3), pages 709-719.
    14. Thomas Mazzuchi & Ehsan Soofi & Refik Soyer, 2008. "Bayes Estimate and Inference for Entropy and Information Index of Fit," Econometric Reviews, Taylor & Francis Journals, vol. 27(4-6), pages 428-456.
    15. Soroush Saghafian & Brian Tomlin, 2016. "The Newsvendor under Demand Ambiguity: Combining Data with Moment and Tail Information," Operations Research, INFORMS, vol. 64(1), pages 167-185, February.
    16. Van den Poel, Dirk & Lariviere, Bart, 2004. "Customer attrition analysis for financial services using proportional hazard models," European Journal of Operational Research, Elsevier, vol. 157(1), pages 196-217, August.
    17. Asadi, Majid & Ebrahimi, Nader & Soofi, Ehsan S., 2005. "Dynamic generalized information measures," Statistics & Probability Letters, Elsevier, vol. 71(1), pages 85-98, January.
    18. Bercher, J.-F., 2012. "A simple probabilistic construction yielding generalized entropies and divergences, escort distributions and q-Gaussians," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(19), pages 4460-4469.
    19. Omid M. Ardakani & Nader Ebrahimi & Ehsan S. Soofi, 2018. "Ranking Forecasts by Stochastic Error Distance, Information and Reliability Measures," International Statistical Review, International Statistical Institute, vol. 86(3), pages 442-468, December.
    20. Plischke, Elmar & Borgonovo, Emanuele & Smith, Curtis L., 2013. "Global sensitivity measures from given data," European Journal of Operational Research, Elsevier, vol. 226(3), pages 536-550.
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