Comparison Study of Nonparametric Tests for Two-Sample Problem through Simulation

In this paper, we propose a new nonparametric test for two sample problem based on the empirical distribution and its quantile functions when any assumptions for the underlying distribution can not be assumed and compare its performance with the similar tests whose statistics are based on the empirical distribution functions. For this, first of all, we review some existing nonparametric tests and then propose a new one. We consider to obtain the null distribution by applying the permutation principle, which is a resampling method. Then we show an example and compare the performance among the nonparametric tests with our test by obtaining empirical powers through a simulation study under the location translation alternative. Also we discuss the bootstrap method which is another resampling method to obtain the null distribution of test statistics. Finally, we comment briefly about the importance of the continuity assumption for the underlying distribution and the topic of our future research.