Comparisons of Largest Order Statistics from Multiple-outlier Gamma Models

Peng Zhao () and N. Balakrishnan ()
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Peng Zhao: Jiangsu Normal University
N. Balakrishnan: McMaster University

Methodology and Computing in Applied Probability, 2015, vol. 17, issue 3, 617-645

Abstract: 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.

Keywords: Hazard rate order; Likelihood ratio order; Star order; Dispersive order; Majorization; p-larger order; Order statistics; Multiple-outlier models; Primary 60E15; Secondary 60K10 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s11009-013-9377-0

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