Testing skew-symmetry based on extreme ranked set sampling

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 t...

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Bibliographic Details
Published in:Statistical papers (Berlin, Germany) Germany), 2021-10, Vol.62 (5), p.2311-2332
Main Authors: Hasanalipour, Parisa, Razmkhah, Mostafa
Format: Article
Language:English
Subjects:
Datasets
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Finance
Insurance
Management
Mathematics and Statistics
Operations Research/Decision Theory
Probability Theory and Stochastic Processes
Regular Article
Sampling
Skewed distributions
Statistics
Statistics for Business
Symmetry
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Summary: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.
ISSN:0932-5026
1613-9798
DOI:10.1007/s00362-020-01183-3