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On a characterization of rectangular distributions


  • Abdelhamid, Sami N.


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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    References listed on IDEAS

    1. Panaretos, John, 1983. "A Generating Model Involving Pascal and Logarithmic Series Distributions," MPRA Paper 6246, University Library of Munich, Germany.
    2. Panaretos, John & Xekalaki, Evdokia, 1986. "On Generalized Binomial and Multinomial Distributions and Their Relation to Generalized Poisson Distributions," MPRA Paper 6248, University Library of Munich, Germany.
    3. Xekalaki, Evdokia & Panaretos, John, 1983. "Identifiability of Compound Poisson Distributions," MPRA Paper 6244, University Library of Munich, Germany.
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