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A quantile approach of Tsallis entropy for order statistics

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  • Kumar, Vikas
  • Rekha,

Abstract

The quantile-based entropy measures possess some unique properties than its distribution function approach. In this article, the concept of quantile based Tsallis entropy is extended for order statistics. We prove that the generalized quantile information between ith order statistics and parent random variable is distribution free. Also the quantile version of Tsallis entropy for residual lifetime has been derived and its monotonicity property is studied. Further some characterization results based on the Tsallis quantile entropy for residual and inactivity time for the series and parallel system have been studied.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:503:y:2018:i:c:p:916-928
    DOI: 10.1016/j.physa.2018.03.025
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    References listed on IDEAS

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    1. Vikas Kumar, 2017. "Characterization results based on dynamic Tsallis cumulative residual entropy," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(17), pages 8343-8354, September.
    2. Kumar, Vikas, 2016. "Some results on Tsallis entropy measure and k-record values," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 667-673.
    3. Thapliyal, Richa & Taneja, H.C. & Kumar, Vikas, 2015. "Characterization results based on non-additive entropy of order statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 417(C), pages 297-303.
    4. Sunoj, S.M. & Sankaran, P.G., 2012. "Quantile based entropy function," Statistics & Probability Letters, Elsevier, vol. 82(6), pages 1049-1053.
    5. 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.
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    1. Tahmasebi, S. & Longobardi, M. & Kazemi, M.R. & Alizadeh, M., 2020. "Cumulative Tsallis entropy for maximum ranked set sampling with unequal samples," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 556(C).
    2. Ahmadi, J. & Fashandi, M., 2019. "Characterization of symmetric distributions based on some information measures properties of order statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 517(C), pages 141-152.
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    4. 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).

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