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Comparisons of Largest Order Statistics from Multiple-outlier Gamma Models

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Listed:
  • Peng Zhao

    (Jiangsu Normal University)

  • N. Balakrishnan

    (McMaster University
    King Abdulaziz University)

Abstract

In this paper, we discuss stochastic comparisons of largest order statistics from multiple-outlier gamma models in terms of different stochastic orderings including the likelihood ratio order, hazard rate order, star order and dispersive order. It is proved, among others, that the weak majorization order between the two scale parameter vectors implies the likelihood ratio order between the largest order statistics, and that the p-larger order between the two scale parameter vectors implies the hazard rate order between the largest order statistics. We also present a general sufficient condition for the star order. The results established here strengthen and generalize some of the results known in the literature. Some numerical examples are also presented to illustrate the established results.

Suggested Citation

  • Peng Zhao & N. Balakrishnan, 2015. "Comparisons of Largest Order Statistics from Multiple-outlier Gamma Models," Methodology and Computing in Applied Probability, Springer, vol. 17(3), pages 617-645, September.
    • Handle: RePEc:spr:metcap:v:17:y:2015:i:3:d:10.1007_s11009-013-9377-0
    DOI: 10.1007/s11009-013-9377-0
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    References listed on IDEAS

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    1. Huaihou Chen & Taizhong Hu, 2008. "Multivariate likelihood ratio orderings between spacings of heterogeneous exponential random variables," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 68(1), pages 17-29, June.
    2. Balakrishnan, N. & Zhao, Peng, 2013. "Hazard rate comparison of parallel systems with heterogeneous gamma components," Journal of Multivariate Analysis, Elsevier, vol. 113(C), pages 153-160.
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    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.
    5. Proschan, F. & Sethuraman, J., 1976. "Stochastic comparisons of order statistics from heterogeneous populations, with applications in reliability," Journal of Multivariate Analysis, Elsevier, vol. 6(4), pages 608-616, December.
    6. Misra, Neeraj & Misra, Amit Kumar, 2013. "On comparison of reversed hazard rates of two parallel systems comprising of independent gamma components," Statistics & Probability Letters, Elsevier, vol. 83(6), pages 1567-1570.
    7. Zhao, Peng & Li, Xiaohu & Balakrishnan, N., 2009. "Likelihood ratio order of the second order statistic from independent heterogeneous exponential random variables," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 952-962, May.
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