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Characterization of symmetric distributions based on some information measures properties of order statistics

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  • Ahmadi, J.
  • Fashandi, M.

Abstract

In this paper, using the completeness properties of certain function sequences, several characterization results of symmetric continuous distributions are established based on various information measures properties of order statistics. It is shown that the equality of some common information measures of upper and lower order statistics is a characteristic property of symmetric distributions. These information measures include Shannon entropy, Rényi entropy, Tsallis entropy, cumulative residual (past) entropy, also some common inaccuracy measures. The results can be used to construct goodness-of-fit test for symmetry.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:517:y:2019:i:c:p:141-152
    DOI: 10.1016/j.physa.2018.11.009
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    References listed on IDEAS

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    1. Vikas Kumar & H. Taneja & R. Srivastava, 2011. "A dynamic measure of inaccuracy between two past lifetime distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 74(1), pages 1-10, July.
    2. Calì, Camilla & Longobardi, Maria & Ahmadi, Jafar, 2017. "Some properties of cumulative Tsallis entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 1012-1021.
    3. Drăgulescu, Adrian & Yakovenko, Victor M., 2001. "Exponential and power-law probability distributions of wealth and income in the United Kingdom and the United States," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 213-221.
    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. Fashandi, M. & Ahmadi, Jafar, 2012. "Characterizations of symmetric distributions based on Rényi entropy," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 798-804.
    6. Chanchal Kundu & Asok Nanda, 2015. "Characterizations based on measure of inaccuracy for truncated random variables," Statistical Papers, Springer, vol. 56(3), pages 619-637, August.
    7. Prem Nath, 1968. "Inaccuracy and coding theory," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 13(1), pages 123-135, December.
    8. Sunoj, S.M. & Krishnan, Aswathy S. & Sankaran, P.G., 2018. "A quantile-based study of cumulative residual Tsallis entropy measures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 494(C), pages 410-421.
    9. 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.
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    Cited by:

    1. Ahmadi, Jafar, 2020. "Characterization results for symmetric continuous distributions based on the properties of k-records and spacings," Statistics & Probability Letters, Elsevier, vol. 162(C).

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