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Sequence of expectations of maximum-order statistics

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  • Huang, J. S.

Abstract

Necessary and sufficient conditions for a given sequence of numbers {[mu]n} to be the expectations of maximum order statistics are usually rather complicated - involving sequences of determinants. We obtain a very simple and intuitive sufficient condition: {[mu]n} is monotonely increasing and for each k, the induced sequence of expectations of the kth largest-order statistics is also monotonely increasing. The condition is obviously necessary. It also leads to a simple bound for the expectation of order statistics, which is surprisingly sharp despite its simplicity.

Suggested Citation

  • Huang, J. S., 1998. "Sequence of expectations of maximum-order statistics," Statistics & Probability Letters, Elsevier, vol. 38(2), pages 117-123, June.
    • Handle: RePEc:eee:stapro:v:38:y:1998:i:2:p:117-123
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    References listed on IDEAS

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    1. Balakrishnan, N., 1990. "Improving the hartley-David-Gumbel bound for the mean of extreme order statistics," Statistics & Probability Letters, Elsevier, vol. 9(4), pages 291-294, April.
    2. Arnold, Barry C., 1985. "p-Norm bounds on the expectation of the maximum of a possibly dependent sample," Journal of Multivariate Analysis, Elsevier, vol. 17(3), pages 316-332, December.
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    2. Kolodynski, Slawomir, 2000. "A note on the sequence of expected extremes," Statistics & Probability Letters, Elsevier, vol. 47(3), pages 295-300, April.

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