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

Keywords

ORDER STATISTICSEXPECTATIONS OF ORDER STATISTICSTRIANGULAR ARRAYMOMENT PROBLEM
Type
Short Communications
Information
Journal of Applied Probability , Volume 11 , Issue 2 , June 1974 , pp. 413 - 416
Copyright
Copyright © Applied Probability Trust 1974 

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References

David, H. A. (1970) Order Statistics. John Wiley, New York.Google Scholar
Hoeffding, W. (1953) On the distribution of the expected values of the order statistics. Ann. Math. Statist. 24, 93–100.Google Scholar
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, 297–303.Google Scholar