Abstract: | There is a close analogy between the problems of testing the hypothesis that two samples come from the same continuous population (the two-sample problem) and testing the hypothesis that a single sample comes from a completely specified continuous distribution (a test of fit problem). In an earlier paper, asymptotic distribution theory was developed for the test of fit problem, under both the hypothesis being tested and interesting alternatives. In this paper, essentially the same asymptotic theory is shown to hold for the two-sample problem. Applications are given. |