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On cumulative residual Kullback–Leibler information

Author

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

Abstract

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

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    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. E.I., Abdul Sathar & K.V., Viswakala, 2019. "Non-parametric estimation of Kullback–Leibler discrimination information based on censored data," Statistics & Probability Letters, Elsevier, vol. 154(C), pages 1-1.
    2. 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.
    3. 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.
    4. Matthieu Garcin, 2023. "Complexity measure, kernel density estimation, bandwidth selection, and the efficient market hypothesis," Papers 2305.13123, arXiv.org.
    5. Mao, Xuegeng & Shang, Pengjian & Wang, Jianing & Yin, Yi, 2020. "Fractional cumulative residual Kullback-Leibler information based on Tsallis entropy," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    6. Matthieu Garcin, 2023. "Complexity measure, kernel density estimation, bandwidth selection, and the efficient market hypothesis," Working Papers hal-04102815, HAL.
    7. Majid Asadi & Karthik Devarajan & Nader Ebrahimi & Ehsan Soofi & Lauren Spirko‐Burns, 2022. "Elaboration Models with Symmetric Information Divergence," International Statistical Review, International Statistical Institute, vol. 90(3), pages 499-524, December.
    8. 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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