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

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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.

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Acknowledgements

The authors express their thanks to the Associate Editor Professor Niansheng Tang and two anonymous reviewers for their insightful comments and helpful suggestions, which have greatly improved the presentation of this manuscript. Yiying Zhang thanks the financial support from the start-up grant at Nankai University, the Fundamental Research Funds for the Central Universities, Nankai University (No. 63201159, No. 63211091), and the financial support from the Natural Science Foundation of Tianjin (No. 20JCQNJC01740). Peng Zhao thanks the support from National Natural Science Foundation of China (11871252) and A Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.

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Authors and Affiliations

  1. School of Statistics and Data Science, LPMC and KLMDASR, Nankai University, Tianjin, 300071, People’s Republic of China

    Yiying Zhang

  2. SpeakIn Technologies Co., Ltd., Shanghai, 200000, People’s Republic of China

    Yanni Hu

  3. School of Mathematics and Statistics and RIMS, Jiangsu Provincial Key Laboratory of Educational Big Data Science and Engineering, Jiangsu Normal University, Xuzhou, 221116, People’s Republic of China

    Peng Zhao

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  1. Yiying Zhang
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  2. Yanni Hu
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  3. Peng Zhao
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Correspondence to Peng Zhao.

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Zhang, Y., Hu, Y. & Zhao, P. Ordering Results on Largest Order Statistics from Multiple-Outlier Gamma Variables. Commun. Math. Stat. 11, 257–282 (2023). https://doi.org/10.1007/s40304-021-00247-6

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  • DOI: https://doi.org/10.1007/s40304-021-00247-6

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