Abstract
For two independent random samples from absolutly continuous distributions Fand G, the problem of testing H0:F=Gagainst H0:F=G and other two-sided alternatives is considered. Then, the rank tests, that are invariant with respect to the remuneration of the samples of size two? are investigated, A description of the problem in geo metric terms' enables us to find the minimal essentially complete class as well as the necessary and sufficient condition of unbiasedness. As a result, we note that some well known tests are not unbiased.
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