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On the Lorenz ordering of order statistics from exponential populations and some applications

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  • Da, Gaofeng
  • Xu, Maochao
  • Balakrishnan, N.

Abstract

In this paper, the variability of order statistics from heterogeneous random samples is studied. It is shown that, without any restriction on the parameters, the variability of order statistics from heterogeneous exponential samples is always larger than that from homogeneous exponential samples in the sense of Lorenz ordering. Finally, some applications to reliability analysis and auction theory are pointed out.

Suggested Citation

  • Da, Gaofeng & Xu, Maochao & Balakrishnan, N., 2014. "On the Lorenz ordering of order statistics from exponential populations and some applications," Journal of Multivariate Analysis, Elsevier, vol. 127(C), pages 88-97.
    • Handle: RePEc:eee:jmvana:v:127:y:2014:i:c:p:88-97
    DOI: 10.1016/j.jmva.2014.02.005
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    References listed on IDEAS

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    1. Cantillon, Estelle, 2008. "The effect of bidders' asymmetries on expected revenue in auctions," Games and Economic Behavior, Elsevier, vol. 62(1), pages 1-25, January.
    2. Arnold, Barry C. & Nagaraja, H. N., 1991. "Lorenz ordering of exponential order statistics," Statistics & Probability Letters, Elsevier, vol. 11(6), pages 485-490, June.
    3. Eric Maskin & John Riley, 2000. "Asymmetric Auctions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 67(3), pages 413-438.
    4. Xu, Maochao & Balakrishnan, N., 2012. "On the sample ranges from heterogeneous exponential variables," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 1-9.
    5. Lefevre, Claude & Utev, Sergey, 2001. "Comparison of individual risk models," Insurance: Mathematics and Economics, Elsevier, vol. 28(1), pages 21-30, February.
    6. Kochar, Subhash & Rojo, Javier, 1996. "Some New Results on Stochastic Comparisons of Spacings from Heterogeneous Exponential Distributions," Journal of Multivariate Analysis, Elsevier, vol. 59(2), pages 272-281, November.
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    Cited by:

    1. Ebrahim Amini-Seresht & Jianfei Qiao & Yiying Zhang & Peng Zhao, 2016. "On the skewness of order statistics in multiple-outlier PHR models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(7), pages 817-836, October.

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