## The Annals of Mathematical Statistics

### Rank Sum Tests of Fit

Chia Kuei Tsao

#### 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