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An extension of the Erdös-Neveu-Rényi theorem with applications to order statistics


  • Kaluszka, M.
  • Okolewski, A.


The necessary and sufficient conditions are given for some stochastic process to be an empirical distribution function from some exchangeable random variables. The result is applied to establish sharp lower and upper bounds for order statistics based on possibly dependent random variables.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:stapro:v:55:y:2001:i:2:p:181-186

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    References listed on IDEAS

    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.
    3. Masaaki Sibuya, 1991. "Bonferroni-type inequalities; Chebyshev-type inequalities for the distributions on [0, n]," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 43(2), pages 261-285, June.
    4. Gascuel, O. & Caraux, G., 1992. "Bounds on expectations of order statistics via extremal dependences," Statistics & Probability Letters, Elsevier, vol. 15(2), pages 143-148, September.
    5. 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.
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    Cited by:

    1. repec:eee:jmvana:v:160:y:2017:i:c:p:1-9 is not listed on IDEAS
    2. Kaluszka, Marek & Okolewski, Andrzej, 2011. "Stability of L-statistics from weakly dependent observations," Statistics & Probability Letters, Elsevier, vol. 81(5), pages 618-625, May.


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