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Summary Asymptotic approximations for the tail probabilities of certain statistics with complex moment generating functions are obtained by the usual methods of large deviation theory. It is pointed out that this approximation should be adequate over the entire range but of particular use for extreme tails. Approximations to the significance levels for one and two sample permutation tests are obtained and these tests are inverted to obtain approximate confidence intervals. These methods are applied to some numerical examples and the results are compared with the exact values and with approximations obtained from Edgeworth expansions.
John Robinson (Wed,) studied this question.