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A characterization of triangular arrays which are expectations of order statistics

Published online by Cambridge University Press:  14 July 2016

Joseph B. Kadane*
Affiliation:
Carnegie-Mellon University, Pittsburgh

Abstract

Necessary and sufficient conditions are found for a triangular array (finite or infinite) to be expected values of order statistics. The conditions are a wellknown recurrence relation, and a moment condition.

Type
Short Communications
Copyright
Copyright © Applied Probability Trust 1974 

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References

David, H. A. (1970) Order Statistics. John Wiley, New York.Google Scholar
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Kadane, J. B. (1971) A moment problem for order statistics. Ann. Math. Statist. 42, 745751.Google Scholar
Konheim, A. G. (1971) A note on order statistics. Amer. Math. Monthly 78, 524.Google Scholar
Mallows, C. (1973) Bounds on distribution functions in terms of expectations of order statistics. Ann. Prob. 1, 297303.Google Scholar