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Kullback–Leibler divergence: A quantile approach

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  • Sankaran, P.G.
  • Sunoj, S.M.
  • Nair, N. Unnikrishnan

Abstract

Divergence measures play an important role in measuring the distance between two probability distribution functions. Kullback–Leibler divergence function is a popular measure in this class. The present paper introduces a quantile based definition of the Kullback–Leibler divergence and study its properties in the context of lifetime data analysis. We also propose the quantile versions of Kullback–Leibler divergence for residual and past lifetime random variables.

Suggested Citation

  • Sankaran, P.G. & Sunoj, S.M. & Nair, N. Unnikrishnan, 2016. "Kullback–Leibler divergence: A quantile approach," Statistics & Probability Letters, Elsevier, vol. 111(C), pages 72-79.
    • Handle: RePEc:eee:stapro:v:111:y:2016:i:c:p:72-79
    DOI: 10.1016/j.spl.2016.01.007
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    References listed on IDEAS

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    1. Di Crescenzo, Antonio & Longobardi, Maria, 2004. "A measure of discrimination between past lifetime distributions," Statistics & Probability Letters, Elsevier, vol. 67(2), pages 173-182, April.
    2. Jessica Kasza & Patty Solomon, 2015. "Comparing Score-Based Methods for Estimating Bayesian Networks Using the Kullback–Leibler Divergence," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(1), pages 135-152, January.
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    4. Prem Nath, 1968. "Inaccuracy and coding theory," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 13(1), pages 123-135, December.
    5. Sunoj, S.M. & Sankaran, P.G., 2012. "Quantile based entropy function," Statistics & Probability Letters, Elsevier, vol. 82(6), pages 1049-1053.
    6. Sunoj, S.M. & Sankaran, P.G. & Nanda, Asok K., 2013. "Quantile based entropy function in past lifetime," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 366-372.
    7. Sankaran, P.G. & Unnikrishnan Nair, N. & Sreedevi, E.P., 2010. "A quantile based test for comparing cumulative incidence functions of competing risks models," Statistics & Probability Letters, Elsevier, vol. 80(9-10), pages 886-891, May.
    8. 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.
    9. P. Sankaran & N. Unnikrishnan Nair, 2009. "Nonparametric estimation of hazard quantile function," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(6), pages 757-767.
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    Cited by:

    1. N. Unnikrishnan Nair & S. M. Sunoj & Rajesh G., 2023. "Relation between Relative Hazard Rates and Residual Divergence with some Applications to Reliability Analysis," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 784-802, February.
    2. Kayal, Suchandan, 2018. "Quantile-based cumulative inaccuracy measures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 329-344.
    3. 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.
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    6. Vikas Kumar & Nirdesh Singh, 2023. "Some Results on Quantile Version of R é $\acute {e}$ nyi Entropy of Order Statistics," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 248-273, February.

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