Abstract
Testing the null hypothesis against the umbrella alternative arises in various practical situations. This article has studied some non parametric tests that may be used for umbrella alternatives and their performance in different symmetric and asymmetric distributions, including long-tailed, short-tailed, and a mixture of two distributions. We have considered viz., Mack and Wolfe test, Hettmansperger and Norton test, Shi test, SU test, and Modified Mack and Wolfe test. The simulation approach assesses the empirical level and power of test statistics. The study shows that the SU and Shi tests have performed almost the same in Normal, Cauchy, Contaminated normal, and mixture distributions. However, the overall performance of the SU test was found to be better than that of other selected tests.
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