A Characterization of Rectangular Distributions

George R. Terrell

doi:10.1214/aop/1176993533

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Home > Journals > Ann. Probab. > Volume 11 > Issue 3 > Article

August, 1983 A Characterization of Rectangular Distributions

George R. Terrell

Ann. Probab. 11(3): 823-826 (August, 1983). DOI: 10.1214/aop/1176993533

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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.

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