Nonparametric testing of distributions—the Epps–Singleton two-sample test using the empirical characteristic function

In statistics, two-sample tests are used to determine whether two sam- ples have been drawn from the same population. An example of such a test is the widely used Kolmogorov–Smirnov two-sample test. There are other distribution- free tests that might be applied in similar occasions. In this article, we describe a two-sample omnibus test introduced by Epps and Singleton, which usually has a greater power than the Kolmogorov–Smirnov test although it is distribution free. The superiority of the Epps–Singleton characteristic function test is illustrated in two examples. We compare the two tests and supplement this contribution with a Stata implementation of the omnibus test.