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.

中文翻译：

---

基于极端排序集抽样测试偏斜对称性

在偏斜分布的一般模型中研究了检验分布的偏斜对称性的问题。为此，首先引入了基于顺序统计的测试，以测试对称性的零假设与分布的偏斜对称性的替代方案。还研究了该测试的一些特性。然后，利用排序集抽样的思想，使用一些适当的抽样方案来测试给定数据集的偏斜对称性。对所提出的测试的功效进行数值比较，以确定在不同情况下排名最佳的集合抽样方案。此外，还与一些现有的非参数检验进行了比较。还使用了一个真实的数据集来说明论文的结果。最后，陈述了一些结论。