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

Author

Listed:
  • Ghobad Barmalzan

    (University of Zabol)

  • Narayanaswamy Balakrishnan

    (McMaster University)

  • Hadi Saboori

    (University of Zabol)

Abstract

Kullback-Leibler divergence (Kℒ)$(\mathcal {K}\mathcal {L})$ 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.

Suggested Citation

  • Ghobad Barmalzan & Narayanaswamy Balakrishnan & Hadi Saboori, 2019. "Characterizations of Proportional Hazard and Reversed Hazard Rate Models Based on Symmetric and Asymmetric Kullback-Leibler Divergences," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 26-38, June.
    • Handle: RePEc:spr:sankhb:v:81:y:2019:i:1:d:10.1007_s13571-017-0144-z
    DOI: 10.1007/s13571-017-0144-z
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    References listed on IDEAS

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    1. Debasis Sengupta & Asok K. Nanda, 1999. "Log‐concave and concave distributions in reliability," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(4), pages 419-433, June.
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