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On sample ranges in multiple-outlier models

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  • Zhao, Peng
  • Zhang, Yiying

Abstract

In this paper, we investigate the ordering properties of sample ranges arising from multiple-outlier models in terms of the reversed hazard rate order and the usual stochastic order. Under the setup of an exponential model, it is shown that the weak majorization order between the two hazard rate vectors is equivalent to the reversed hazard rate order between exponential sample ranges; the p-larger order between two hazard rate vectors implies the usual stochastic order between exponential sample ranges. Under the setup of a proportional hazard rate (PHR) model, we prove that the majorization order between two parameter vectors implies the usual stochastic order between sample ranges. The results established here strengthen and generalize some of the results known in the literature. Some numerical examples are provided to illustrate the theoretical results.

Suggested Citation

  • Zhao, Peng & Zhang, Yiying, 2012. "On sample ranges in multiple-outlier models," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 335-349.
    • Handle: RePEc:eee:jmvana:v:111:y:2012:i:c:p:335-349
    DOI: 10.1016/j.jmva.2012.04.010
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    References listed on IDEAS

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    1. Genest, Christian & Kochar, Subhash C. & Xu, Maochao, 2009. "On the range of heterogeneous samples," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1587-1592, September.
    2. Zhao, Peng & Balakrishnan, N., 2009. "Mean residual life order of convolutions of heterogeneous exponential random variables," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1792-1801, September.
    3. Kochar, Subhash & Xu, Maochao, 2010. "On the right spread order of convolutions of heterogeneous exponential random variables," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 165-176, January.
    4. 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. Antonia Castaño-Martínez & Gema Pigueiras & Miguel A. Sordo, 2021. "On the Increasing Convex Order of Relative Spacings of Order Statistics," Mathematics, MDPI, vol. 9(6), pages 1-12, March.
    2. 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.
    3. Ding, Weiyong & Da, Gaofeng & Zhao, Peng, 2013. "On sample ranges from two sets of heterogenous random variables," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 63-73.

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