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On a characterization of rectangular distributions

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  • Abdelhamid, Sami N.

Abstract

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.

Suggested Citation

  • Abdelhamid, Sami N., 1985. "On a characterization of rectangular distributions," Statistics & Probability Letters, Elsevier, vol. 3(5), pages 235-238, September.
  • Handle: RePEc:eee:stapro:v:3:y:1985:i:5:p:235-238
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