Maximum test and adaptive test for the general two-sample problem

An extension of the omnibus test statistic of Ebner et al. [A new omnibus test of fit based on a characterization of the uniform distribution. Statistics. 2022;56:1364-1384. doi: 10.1080/02331888.2022.2133121] is considered for the general two-sample alternative. In addition, using the extension this paper introduces a maximum test statistic and an adaptive test statistic for testing the equality of two distributions. The power performance in various situations is investigated for continuous and discrete distributions. Simulation studies based on Monte-Carlo show that the proposed test statistics are good competitors of the existing nonparametric test statistics. The proposed test statistic displays outstanding performance in certain situations, and is illustrated using real data. Finally, we offer some concluding remarks.