(Received October 14, 1991; revised September 13, 1995)
Abstract. Critchlow (1992, J. Statist. Plann. Inference, 32, 325-346) proposed a method of a unified construction of a class of rank tests. In this paper, we introduce a convex sum distance and prove the limiting normality of the test statistics for the two-sample problem derived by his method.
Key words and phrases: Convex sum distance, transposition property, limiting normality.