A generalized wilcoxon-mann-whitney statistic

Abstract

We develop a simple but useful generalization of the classical Wilcoxon-Mann-Whitney statistic. A normal approximation and a recurrence for the exact distribution of this generalization are available. The statistic has potential application in nonparametric discriminant analysis.

Keywords:

• U-Statistic
• rank statistic
• stochastic ordering
• permutation test
• sub-sample test
• distribution-free test
• Pitman's asymptotic relative efficiency
• exact distribution
• recurrence
• generating function
• discriminant analysis
• classification