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COMPARISONS ON LARGEST ORDER STATISTICS FROM HETEROGENEOUS GAMMA SAMPLES

Published online by Cambridge University Press:  09 March 2020

Ting Zhang ,
Yiying Zhang Open the ORCID record for Yiying Zhang [Opens in a new window]  and
Peng Zhao Open the ORCID record for Peng Zhao [Opens in a new window]
Ting Zhang
Affiliation:
School of Statistics and Data Science, LPMC and KLMDASR, Nankai University, Tianjin 300071, China E-mail: yyzhang@nankai.edu.cn
Yiying Zhang
Affiliation:
School of Statistics and Data Science, LPMC and KLMDASR, Nankai University, Tianjin 300071, China E-mail: yyzhang@nankai.edu.cn
Peng Zhao
Affiliation:
School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, China
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Abstract

This paper deals with stochastic comparisons of the largest order statistics arising from two sets of independent and heterogeneous gamma samples. It is shown that the weak supermajorization order between the vectors of scale parameters together with the weak submajorization order between the vectors of shape parameters imply the reversed hazard rate ordering between the corresponding maximum order statistics. We also establish sufficient conditions of the usual stochastic ordering in terms of the p-larger order between the vectors of scale parameters and the weak submajorization order between the vectors of shape parameters. Numerical examples and applications in auction theory and reliability engineering are provided to illustrate these results.

Keywords

gamma distributionlargest order statisticsmajorizationp-larger orderreversed hazard rate orderusual stochastic order
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 35 , Issue 3 , July 2021 , pp. 611 - 630
Copyright
© Cambridge University Press 2020

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