## The Annals of Mathematical Statistics

- Ann. Math. Statist.
- Volume 26, Number 1 (1955), 94-104.

### Rank Sum Tests of Fit

#### Abstract

This paper suggests several `goodness of fit' test criteria, all having a linear form. The moment generating function and the limiting distribution of this linear form are obtained in Section 2. The best test criterion of this form for testing a simple hypothesis $H_0$ against a simple alternative hypothesis $H_1$ is shown, in Section 3, to be in general not independent of $H_1$. The remainder of this paper deals with a special case of the linear form, that is, the rank sum test criterion. The distribution of this test criterion is derived in Section 4, its consistency is proved in Section 5, and some numerical asymptotic efficiencies are calculated in Section 6. Within a certain class of tests, the present test is shown, in Section 7, to be uniformly most powerful for a special family of alternatives.

#### Article information

**Source**

Ann. Math. Statist., Volume 26, Number 1 (1955), 94-104.

**Dates**

First available in Project Euclid: 28 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aoms/1177728596

**Digital Object Identifier**

doi:10.1214/aoms/1177728596

**Mathematical Reviews number (MathSciNet)**

MR68788

**Zentralblatt MATH identifier**

0065.12102

**JSTOR**

links.jstor.org

#### Citation

Tsao, Chia Kuei. Rank Sum Tests of Fit. Ann. Math. Statist. 26 (1955), no. 1, 94--104. doi:10.1214/aoms/1177728596. https://projecteuclid.org/euclid.aoms/1177728596