On a characterization of rectangular distributions |
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| Authors: | Sami N Abdelhamid |
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| Affiliation: | Department of Mathematics, Kuwait University, Kuwait |
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| Abstract: | ![]()
Let (X(1), X(2)) be the order statistics of a sample of size 2 from a population having density ?. It is well known that X(1) and X(2) are positively correlated. We show that cov(X(1), X(2)) has an upper bound which is attained if and only if ? is rectangular density on (0, 1). Our proof uses a 2-dimensional extension of a result due to Polya. |
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| Keywords: | characterizations of uniform distribution order statistics covariance |
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