A Characterization of Rectangular Distributions

Other literature type English OPEN
Terrell, George R. (1983)
  • Publisher: The Institute of Mathematical Statistics
  • Journal: (issn: 0091-1798)
  • Related identifiers: doi: 10.1214/aop/1176993533
  • Subject: Rectangular distribution | uniform distribution | order statistics | Legendre polynomials | coefficient of correlation | 60E15 | 62E10

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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