Percentage points are given for the asymptotic distributions of the goodness-of-fit statistics W², U² and A², for the cases where the distribution tested is (a) normal, with mean or variance, or both, unknown; (b) exponential, with scale parameter unknown. Some exact means and variances are also given. The distributions can be expressed as a sum of weighted chi-square variables; the weights are calculated, and the higher cumulants can then be found. The first four cumulants are used to approximate the distributions and give the percentage points.
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Michael A. Stephens (1976) studied this question.