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Inequalities for expected extreme order statistics

Author

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  • de la Cal, J.
  • Cárcamo, J.

Abstract

We obtain one-sided bounds for differences of expected extreme order statistics, when the involved random vectors have (integrable) independent components, and the marginal distributions satisfy a suitable condition. The general results are applied to random samples whose parent distributions are binomial, Poisson, and negative binomial distributions having the same mean. We also derive a method to give lower (upper) bounds for expected maxima (minima) of integrable independent random variables.

Suggested Citation

  • de la Cal, J. & Cárcamo, J., 2005. "Inequalities for expected extreme order statistics," Statistics & Probability Letters, Elsevier, vol. 73(3), pages 219-231, July.
    • Handle: RePEc:eee:stapro:v:73:y:2005:i:3:p:219-231
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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.
    3. 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.
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    Cited by:

    1. Baíllo, A. & Berrendero, J.R. & Cárcamo, J., 2009. "Tests for zero-inflation and overdispersion: A new approach based on the stochastic convex order," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2628-2639, May.

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