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Bounds for order statistics based on dependent variables with given nonidentical distributions

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  • Rychlik, Tomasz

Abstract

We consider order statistics based on possibly dependent nonidentically distributed random variables with fixed one-dimensional distributions. We state necessary and sufficient conditions on marginal distributions for existence of a random vector such that the distribution function of a given order statistic attains a general bound.

Suggested Citation

  • Rychlik, Tomasz, 1995. "Bounds for order statistics based on dependent variables with given nonidentical distributions," Statistics & Probability Letters, Elsevier, vol. 23(4), pages 351-358, June.
    • Handle: RePEc:eee:stapro:v:23:y:1995:i:4:p:351-358
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    References listed on IDEAS

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    1. Rychlik, Tomasz, 1992. "Stochastically extremal distributions of order statistics for dependent samples," Statistics & Probability Letters, Elsevier, vol. 13(5), pages 337-341, April.
    2. Caraux, G. & Gascuel, O., 1992. "Bounds on distribution functions of order statistics for dependent variates," Statistics & Probability Letters, Elsevier, vol. 14(2), pages 103-105, May.
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    Cited by:

    1. Okolewski, Andrzej, 2017. "Extremal properties of order statistic distributions for dependent samples with partially known multidimensional marginals," Journal of Multivariate Analysis, Elsevier, vol. 160(C), pages 1-9.
    2. Kaluszka, M. & Okolewski, A., 2001. "An extension of the Erdös-Neveu-Rényi theorem with applications to order statistics," Statistics & Probability Letters, Elsevier, vol. 55(2), pages 181-186, November.
    3. Navarro, Jorge & Ruiz, Jose M. & Sandoval, Carlos J., 2005. "A note on comparisons among coherent systems with dependent components using signatures," Statistics & Probability Letters, Elsevier, vol. 72(2), pages 179-185, April.
    4. Navarro, Jorge & Rychlik, Tomasz, 2007. "Reliability and expectation bounds for coherent systems with exchangeable components," Journal of Multivariate Analysis, Elsevier, vol. 98(1), pages 102-113, January.

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