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THE LIMITING NORMALITY OF THE TEST STATISTIC

FOR THE TWO-SAMPLE PROBLEM INDUCED

BY A CONVEX SUM DISTANCE

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KAORU FUEDA

*Graduate School of Mathematics, Kyushu University,*

Higashi-ku, Hakozaki 6-10-1, Fukuoka 812, Japan
(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.

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