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August, 1983 A Characterization of Rectangular Distributions
George R. Terrell
Ann. Probab. 11(3): 823-826 (August, 1983). DOI: 10.1214/aop/1176993533


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.


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George R. Terrell. "A Characterization of Rectangular Distributions." Ann. Probab. 11 (3) 823 - 826, August, 1983.


Published: August, 1983
First available in Project Euclid: 19 April 2007

zbMATH: 0513.62016
MathSciNet: MR704575
Digital Object Identifier: 10.1214/aop/1176993533

Primary: 60E15
Secondary: 62E10

Keywords: coefficient of correlation , Legendre polynomials , order statistics , Rectangular distribution , uniform distribution

Rights: Copyright © 1983 Institute of Mathematical Statistics

Vol.11 • No. 3 • August, 1983
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