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Quantile based entropy function in past lifetime

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  • Sunoj, S.M.
  • Sankaran, P.G.
  • Nanda, Asok K.

Abstract

Di Crescenzo and Longobardi (2002) introduced a measure of uncertainty in past lifetime distributions and studied its relationship with residual entropy function. In the present paper, we introduce a quantile version of the entropy function in past lifetime and study its properties. Unlike the measure of uncertainty given in Di Crescenzo and Longobardi (2002) the proposed measure uniquely determines the underlying probability distribution. The measure is used to study two nonparametric classes of distributions. We prove characterizations theorems for some well known quantile lifetime distributions.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:1:p:366-372
    DOI: 10.1016/j.spl.2012.09.016
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    References listed on IDEAS

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    1. Navarro, J. & Sunoj, S.M. & Linu, M.N., 2011. "Characterizations of bivariate models using dynamic Kullback-Leibler discrimination measures," Statistics & Probability Letters, Elsevier, vol. 81(11), pages 1594-1598, November.
    2. Bartoszewicz, Jaroslaw, 2009. "On a representation of weighted distributions," Statistics & Probability Letters, Elsevier, vol. 79(15), pages 1690-1694, August.
    3. Asok Nanda & Prasanta Paul, 2006. "Some Properties of Past Entropy and their Applications," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 64(1), pages 47-61, August.
    4. Sunoj, S.M. & Sankaran, P.G., 2012. "Quantile based entropy function," Statistics & Probability Letters, Elsevier, vol. 82(6), pages 1049-1053.
    5. 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.
    6. 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. Kayal, Suchandan, 2018. "Quantile-based cumulative inaccuracy measures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 329-344.
    2. Nanda, Asok K. & Sankaran, P.G. & Sunoj, S.M., 2014. "Rényi’s residual entropy: A quantile approach," Statistics & Probability Letters, Elsevier, vol. 85(C), pages 114-121.
    3. Aswathy S. Krishnan & S. M. Sunoj & P. G. Sankaran, 2019. "Quantile-based reliability aspects of cumulative Tsallis entropy in past lifetime," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(1), pages 17-38, January.
    4. Kumar, Vikas & Rekha,, 2018. "A quantile approach of Tsallis entropy for order statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 916-928.
    5. 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.
    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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