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Skewness coefficients based on OWA functions with applications in tests of symmetry
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DOI：10.1016/j.fss.2026.110039.png)
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Abstract
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Different data summaries have been studied in the field of aggregation theory. Among these data summaries, skewness coefficients play a central role in quantifying departures from symmetry in the distribution of a random variable. In this paper, we introduce a family of coefficients whose sample counterparts are constructed using OWA functions. We investigate the conditions under which the proposed coefficients satisfy the axiomatic properties of a skewness coefficient established by Oja. In addition, we derive the asymptotic distribution of their sample version and use it to develop tests of symmetry. Both theoretical results and simulation studies are provided to assess the performance of the presented tests.
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