A MAX-TYPE BAUMGARTNER STATISTIC FOR THE TWO-SAMPLE PROBLEM AND ITS POWER COMPARISON

In this paper, we focus on the univariate two-sample Baumgartner statistic and propose a modification of the B statistic for the shifted-scale parameter. A nonparametric rank test based on the Baumgartner statistic was used to test location, scale, and location-scale parameters. Critical values of the test statistics were evaluated; limiting distributions were derived under the null hypothesis. We investigated the power of the proposed statistics by simulation studies. The results of our simulations indicated that the B2 statistic was superior to the B1 statistic for the shifted scale parameters when the sample sizes were equal under symmetric distributions. The differences between these two statistics were small when the sample sizes were unequal. The B2 statistic is more efficient than other nonparametric statistics.