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Testing skew-symmetry based on extreme ranked set sampling

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Abstract

The problem of testing skew-symmetry of a distribution is studied in a general model of skew distributions. Toward this end, an order statistic-based test is first introduced to test the null hypotheses of symmetry against the alternative of skew-symmetry of a distribution. Some properties of this test are also studied. Then, using the idea of ranked set sampling, some appropriate sampling schemes are used to test skew-symmetry of a given data set. The power of the proposed tests are compared numerically to determine the best ranked set sampling scheme in different situations. Further, a comparison with some of existing non-parametric tests has been done. A real data set is also used to illustrate the results of the paper. Finally, some conclusions are stated.

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Acknowledgements

The authors would like to thank an anonymous referees and the associate editor for their useful comments and constructive criticisms on the original version of this manuscript which led to this considerably improved version. This research was supported by a grant from Ferdowsi University of Mashhad (No. 2/52143).

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  1. Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, P. O. Box 1159, Mashhad, 91775, Iran

    Parisa Hasanalipour & Mostafa Razmkhah

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  1. Parisa Hasanalipour
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  2. Mostafa Razmkhah
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Correspondence to Mostafa Razmkhah.

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Hasanalipour, P., Razmkhah, M. Testing skew-symmetry based on extreme ranked set sampling. Stat Papers 62, 2311–2332 (2021). https://doi.org/10.1007/s00362-020-01183-3

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  • DOI: https://doi.org/10.1007/s00362-020-01183-3

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