A simple recursive formula is used to generate the distribution of the MWW U-statistic under alternatives of the form K 1: G – F k ,1 ≠ k < 0, and K 2: G – 1− (1 − F) k , 1 ≠ k > 0, and it is pointed out that many of these alternatives are of interest in life testing, reliability testing and related fields. Tables are given for the case G = 1 – (1 − F) k for 4 ≤ n, m ≤ 8 and k = 2,3,4,6,9,12 and it is shown that these tables can also be used when G = F k and when 0 < k < 1.
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Roger A. Shorack (1967) studied this question.