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Distributions and expectations of order statistics for possibly dependent random variables. (English) Zbl 0790.62048
Summary: The class of all possible distribution functions of each order statistic for a sample of possibly dependent, identically distributed random variables is characterized. An effective method of determination of the extreme values for the expectation and variance of an arbitrary Borel function of order statistics is presented and applied for calculating the moments in the case of uniformly distributed random variables.

62G30 Order statistics; empirical distribution functions
62E10 Characterization and structure theory of statistical distributions
60E05 Probability distributions: general theory
Full Text: DOI
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