Sankhya B

, Volume 81, Issue 1, pp 26–38 | Cite as

Characterizations of Proportional Hazard and Reversed Hazard Rate Models Based on Symmetric and Asymmetric Kullback-Leibler Divergences

  • Ghobad BarmalzanEmail author
  • Narayanaswamy Balakrishnan
  • Hadi Saboori


Kullback-Leibler divergence \((\mathcal {K}\mathcal {L})\) is widely used for selecting the best model from a given set of candidate parametrized probabilistic models as an approximation to the true density function h(·). In this paper, we obtain a necessary and sufficient condition to determine proportional hazard and reversed hazard rate models based on symmetric and asymmetric Kullback-Leibler divergences. Obtained results show that if h belongs to proportional hazard rate (reversed hazard) model, then the Kullback-Leibler divergence between h and baseline density function, f0, is independent of the choice of ξ, the cut point of left (right) truncated distribution.

Keywords and phrases

Symmetric Kullback-Leibler divergence Asymmetric Kullback-Leibler divergence Proportional hazard rate model Proportional reversed hazard rate model. 

AMS (2000) subject classification

Primary 62E10 Secondary 62F30 


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Copyright information

© Indian Statistical Institute 2017

Authors and Affiliations

  • Ghobad Barmalzan
    • 1
    Email author
  • Narayanaswamy Balakrishnan
    • 2
  • Hadi Saboori
    • 1
  1. 1.Department of StatisticsUniversity of ZabolZabolIran
  2. 2.Department of Mathematics and StatisticsMcMaster UniversityHamiltonCanada

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