Annals of Probability

A Characterization of Rectangular Distributions

George R. Terrell

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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


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