## The Annals of Mathematical Statistics

### On the Large Sample Properties of a Generalized Wilcoxon-Mann-Whitney Statistic

A. P. Basu

#### Abstract

Let there be two independent samples of sizes $m$ and $n$ respectively from two populations with continuous cdf's $F(x)$ and $G(y)$. To test the equality of the two populations Sobel [19], has proposed the statistic $V^{m,n}_r$ (to be defined later) based on the first $r$ ordered observations only. In this paper the large sample properties of $V^{m,n}_r$ have been studied. The test is compared with other "$r$ out of $N$" tests by computing the appropriate asymptotic relative efficiencies. The test statistic is found to be quite satisfactory in all the cases considered and is particularly suitable for location alternatives.

#### Article information

Source
Ann. Math. Statist., Volume 38, Number 3 (1967), 905-915.

Dates
First available in Project Euclid: 27 April 2007

https://projecteuclid.org/euclid.aoms/1177698884

Digital Object Identifier
doi:10.1214/aoms/1177698884

Mathematical Reviews number (MathSciNet)
MR212951

Zentralblatt MATH identifier
0149.15006

JSTOR