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On cumulative residual Kullback–Leibler information


  • Park, Sangun
  • Rao, Murali
  • Shin, Dong Wan


Some extensions of entropy and KL information to the survival function have been recently proposed. We first compare some extensions of KL information and provide a criterion in choosing one among those extensions. Then we study moment constraints for maximum cumulative residual entropy distribution (Rao et al., 2004) in view of the relation between the cumulative residual entropy difference and cumulative residual Kullback–Leibler (KL) information. We further discuss the estimation methods and suggest a weighted cumulative residual entropy. Finally, we discuss the application of the estimated cumulative residual KL information as a goodness of fit test statistic with numerical examples.

Suggested Citation

  • Park, Sangun & Rao, Murali & Shin, Dong Wan, 2012. "On cumulative residual Kullback–Leibler information," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 2025-2032.
  • Handle: RePEc:eee:stapro:v:82:y:2012:i:11:p:2025-2032 DOI: 10.1016/j.spl.2012.06.015

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    References listed on IDEAS

    1. Theil, Henri, 1980. "The entropy of the maximum entropy distribution," Economics Letters, Elsevier, vol. 5(2), pages 145-148.
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    Cited by:

    1. Park, Sangun & Pakyari, Reza, 2015. "Cumulative residual Kullback–Leibler information with the progressively Type-II censored data," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 287-294.
    2. Chahkandi, M. & Noughabi, H. Alizadeh, 2016. "Testing exponentiality of the residual life, based on dynamic cumulative residual entropy," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 1-11.


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