Two new distribution-free two-sample tests for versatile alternative

摘要

This paper introduces two alternative distribution-free tests for the combined classical-location-scale and Lehmann alternatives, known as the versatile alternative. Recently, two such statistics were proposed, one based on the Euclidean distance and the other based on the Mahalanobis distance, combining the three test statistics, the Wilcoxon statistic for the location parameter, the Ansari-Bradley statistic for the scale parameter and a Savage-type statistic for the Lehmann alternative. However, noting that there is some practical advantage of using the Mood statistic in place of the Ansari-Bradley statistic, two new tests are designed in the present paper. We derive the limiting distributions of the proposed statistics and investigate their power performances in different situations. Simulation studies based on Monte-Carlo also show that the proposed tests are good competitors of the existing tests and have some advantage in certain situations. We include illustrations based on real-life data and finally offer some concluding remarks.