Ordering Results on Largest Order Statistics from Multiple-Outlier Gamma Variables

Abstract

In this article, we carry out stochastic comparisons on the maximum order statistics arising from two batches of multiple-outlier gamma random variables with different shape and scale parameters. It is proved that, under certain conditions, the majorization order between the vectors of shape parameters together with the weak majorization order [p-larger order] between the vectors of scale parameters implies the likelihood ratio order [hazard rate order] between the largest order statistics. The results established here strengthen and generalize some known ones in the literature.

Keywords

Gamma distribution / Stochastic orders / Largest order statistics / Majorization / p-Larger order

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Funding

National Natural Science Foundation of China(11871252)

Nankai University(63201159)