On a characterization of rectangular distributions
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.
Volume (Year): 3 (1985)
Issue (Month): 5 (September)
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