A class of nonparametric tests for the two-sample problem based on order statistics

In this paper, a new class of distribution-free statistics based on order statistics from two independent samples is introduced to test the equality of two continuous distributions. The null distributions are obtained, and the symmetry property of the proposed test statistics is studied. The exact power functions of the new class of tests under the Lehmann alternative family are derived. Extensions of the proposed class of test statistics to situations with unequal sample sizes are discussed. We also study the power performance of the proposed test under the location-shift and scale-shift alternatives using Monte Carlo simulations. We observe that the power performance of the new class of test procedures is comparable to some commonly used nonparametric tests under various scenarios, which indicates that the new class of test procedures can be a good alternative to those classic nonparametric tests for the two-sample problem.