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Characterizations of symmetric distributions using equi-distributions and moment properties of functions of order statistics

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Abstract

Several characterizations of symmetry of a probability distribution are provided. These include the equality in distributions of symmetrically chosen upper and lower order statistics, symmetric spacings of order statistics, and quasi-midranges. Characterizations of symmetry based on the moment properties of order statistics, quasi-midranges and spacings are established. Some characterizations in terms of moments of the underlying distribution are also given.

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Acknowledgements

The authors would like to thank two anonymous referees for their useful comments and suggestions on the previous version. The research of J. Ahmadi was supported by Ferdowsi University of Mashhad (Grant number 2/50362).

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Authors and Affiliations

  1. Department of Statistics, Ferdowsi University of Mashhad, P. O. Box 1159, Mashhad, 91775, Iran

    Jafar Ahmadi & M. Fashandi

  2. Division of Biostatistics, The Ohio State University, Columbus, OH, 43210, USA

    H. N. Nagaraja

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  1. Jafar Ahmadi
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  2. M. Fashandi
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  3. H. N. Nagaraja
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Correspondence to Jafar Ahmadi.

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Ahmadi, J., Fashandi, M. & Nagaraja, H.N. Characterizations of symmetric distributions using equi-distributions and moment properties of functions of order statistics. RACSAM 114, 90 (2020). https://doi.org/10.1007/s13398-020-00820-8

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  • DOI: https://doi.org/10.1007/s13398-020-00820-8

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