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Bounds on distribution functions of order statistics for dependent variates

Author

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  • Caraux, G.
  • Gascuel, O.

Abstract

Upper and lower bounds are given for FXr:n, the distribution function of the rth order statistic from n possibly dependent random variables. We show that these bounds may be reached when the random variables have a common distribution function. For any distribution function F we may construct a set of n exchangeable variates (with c.d.f. F), whose dependency structure is such that the bounds are attained.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:14:y:1992:i:2:p:103-105
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    Citations

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    Cited by:

    1. Escudero, Laureano F. & Ortega, Eva-María, 2008. "Actuarial comparisons for aggregate claims with randomly right-truncated claims," Insurance: Mathematics and Economics, Elsevier, vol. 43(2), pages 255-262, October.
    2. 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.
    3. Jing Cao & Ann Moosman & Valen E. Johnson, 2010. "A Bayesian Chi-Squared Goodness-of-Fit Test for Censored Data Models," Biometrics, The International Biometric Society, vol. 66(2), pages 426-434, June.
    4. Papadatos, Nickos, 2001. "Distribution and expectation bounds on order statistics from possibly dependent variates," Statistics & Probability Letters, Elsevier, vol. 54(1), pages 21-31, August.
    5. Ying Yuan & Valen E. Johnson, 2012. "Goodness-of-Fit Diagnostics for Bayesian Hierarchical Models," Biometrics, The International Biometric Society, vol. 68(1), pages 156-164, March.
    6. Tomasz Rychlik, 2001. "Stability of Order Statistics under Dependence," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(4), pages 877-894, December.
    7. D. Blanke & D. Bosq, 2018. "Polygonal smoothing of the empirical distribution function," Statistical Inference for Stochastic Processes, Springer, vol. 21(2), pages 263-287, July.
    8. 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.
    9. 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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