## The Annals of Mathematical Statistics

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

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

#### 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

**Permanent link to this document**

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**

links.jstor.org

#### Citation

Basu, A. P. On the Large Sample Properties of a Generalized Wilcoxon-Mann-Whitney Statistic. Ann. Math. Statist. 38 (1967), no. 3, 905--915. doi:10.1214/aoms/1177698884. https://projecteuclid.org/euclid.aoms/1177698884