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On a characterization of rectangular distributions

  • Abdelhamid, Sami N.
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    Let (X(1), X(2)) be the order statistics of a sample of size 2 from a population having density [latin small letter f with hook]. 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 [latin small letter f with hook] is rectangular density on (0, 1). Our proof uses a 2-dimensional extension of a result due to Polya.

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    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 3 (1985)
    Issue (Month): 5 (September)
    Pages: 235-238

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    Handle: RePEc:eee:stapro:v:3:y:1985:i:5:p:235-238
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