The two-sample problem is: given samples X and Y from two distributions, test whether the two underlying distributions are the same. One of the most common classical nonparametric approach is the Kolmogorov-Smirnov test.
The two-sample problem is to compare parameters of two (potentially) different populations given samples of them.
An extreme case concerns testing whether the populations have the same distribution. A classical solution is the Kolmogorov-Smirnov test.
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