## The Annals of Statistics

- Ann. Statist.
- Volume 9, Number 6 (1981), 1248-1257.

### Likelihood Ratio Tests for and Against a Stochastic Ordering Between Multinomial Populations

Tim Robertson and F. T. Wright

#### Abstract

Likelihood ratio tests concerning the parameters of two multinomial populations are discussed. A stochastic ordering restriction is considered as a one sided alternative to equality. The one and two sample tests for equality versus stochastic ordering and stochastic ordering versus all alternatives are derived and their large sample distributions are obtained. The large sample distributions are mixtures of chi-squared distributions. The tests developed provide discrete analogues for the one sided Mann-Whitney-Wilcoxon and Kolmogorov-Smirnov tests.

#### Article information

**Source**

Ann. Statist., Volume 9, Number 6 (1981), 1248-1257.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aos/1176345641

**Digital Object Identifier**

doi:10.1214/aos/1176345641

**Mathematical Reviews number (MathSciNet)**

MR630107

**Zentralblatt MATH identifier**

0474.62038

**JSTOR**

links.jstor.org

**Subjects**

Primary: 62G10: Hypothesis testing

Secondary: 62E20: Asymptotic distribution theory

**Keywords**

Stochastic ordering multinomial distributions chi-bar-squared tests likelihood ratio asymptotic results

#### Citation

Robertson, Tim; Wright, F. T. Likelihood Ratio Tests for and Against a Stochastic Ordering Between Multinomial Populations. Ann. Statist. 9 (1981), no. 6, 1248--1257. doi:10.1214/aos/1176345641. https://projecteuclid.org/euclid.aos/1176345641