In this paper, we introduce a new nonparametric test of symmetry based on the empirical overlap coefficient using kernel density estimation. Our investigation reveals that the new test is more powerful than the runs test of symmetry proposed by McWilliams [31]. Intensive simulation is conducted to examine the power of the proposed test. Data from a level I Trauma center are used to illustrate the procedures developed in this paper.
This paper investigates point and interval estimation for some well-known measures of overlap. Two types of sampling procedures, namely, Simple Random Sample and Ranked Set Sample from two Lomax populations with different shape parameters are considered. Simulation studies are conducted to get insight on the performance of the proposed estimators. Taylor series approximations as well as bootstrap method are used to construct confidence intervals for those measures.
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