Generalizing the Mann-Whitney-Wilcoxon statistic

We present a generalization of the classical Mann-Whitney-Wilcoxon (MWW) st atistic for testing stochastic ordering between two distributions. Our clas s of statistics includes as special cases the generalizations of the MWW st atistic by Kochar (1978); Deshpande and Kochar (1980); Stephenson and Ghosh (1985); Shetty and Govindarajulu (1988); Shetty and Bhat (1993); Ahmad (19 96); Kumar (1997) and Priebe and Cowen (1999). We establish the asymptotic normality and demonstrate the admissibility of the generalization in the se nse of Pitman's asymptotic efficacy. Corresponding distribution-free confid ence intervals are derived and a generalization of the Wilcoxon signed rank statistic For testing the center of a symmetric, univariate, continuous di stribution is obtained.