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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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    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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