A uniform saddlepoint expansion for the null‐distribution of the wilcoxon‐mann‐whitney statistic

The authors give the exact coefficient of 1/N in a saddlepoint approximation to the Wilcoxon‐Mann‐Whitney null‐distribution. This saddlepoint approximation is obtained from an Edgeworth approximation to the exponentially tilted distribution. Moreover, the rate of convergence of the relative error is uniformly of order O (1/N) in a large deviation interval as defined in Feller (1971). The proposed method for computing the coefficient of 1/N can be used to obtain the exact coefficients of 1/Nⁱ, for any i. The exact formulas for the cumulant generating function and the cumulants, needed for these results, are those of van Dantzig (1947‐1950).