## Annals of Probability

- Ann. Probab.
- Volume 11, Number 3 (1983), 823-826.

### A Characterization of Rectangular Distributions

#### Abstract

It is well known that the smaller and the larger of a random sample of size two are positively correlated. The coefficient of correlation is at most one-half, and the upper bound is attained only for rectangular distributions.

#### Article information

**Source**

Ann. Probab., Volume 11, Number 3 (1983), 823-826.

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aop/1176993533

**Digital Object Identifier**

doi:10.1214/aop/1176993533

**Mathematical Reviews number (MathSciNet)**

MR704575

**Zentralblatt MATH identifier**

0513.62016

**JSTOR**

links.jstor.org

**Subjects**

Primary: 60E15: Inequalities; stochastic orderings

Secondary: 62E10: Characterization and structure theory

**Keywords**

Rectangular distribution uniform distribution order statistics Legendre polynomials coefficient of correlation

#### Citation

Terrell, George R. A Characterization of Rectangular Distributions. Ann. Probab. 11 (1983), no. 3, 823--826. doi:10.1214/aop/1176993533. https://projecteuclid.org/euclid.aop/1176993533