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Monotonicity properties of certain expected extreme order statistics

Author

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  • de la Cal, Jesús
  • Valle, Ana M.

Abstract

If X1([theta]),...,Xn([theta]) are independent random variables having discrete distributions depending on a positive parameter [theta][set membership, variant](0,[rho]) and satisfying appropriate assumptions, the expected extreme order statistics EXn:n([theta]) and EX1:n([theta]) have nice monotonicity properties. Such properties extend to random extreme order statistics, but not to intermediate order statistics.

Suggested Citation

  • de la Cal, Jesús & Valle, Ana M., 2001. "Monotonicity properties of certain expected extreme order statistics," Statistics & Probability Letters, Elsevier, vol. 52(3), pages 313-319, April.
    • Handle: RePEc:eee:stapro:v:52:y:2001:i:3:p:313-319
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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. Huang, J. S., 1997. "Sharp bounds for the expected value of order statistics," Statistics & Probability Letters, Elsevier, vol. 33(1), pages 105-107, April.
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    Cited by:

    1. de la Cal, J. & Cárcamo, J., 2005. "Inequalities for expected extreme order statistics," Statistics & Probability Letters, Elsevier, vol. 73(3), pages 219-231, July.

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