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SOME NEW RESULTS ON THE LARGEST ORDER STATISTICS FROM MULTIPLE-OUTLIER GAMMA MODELS

Published online by Cambridge University Press:  16 July 2015

Peng Zhao ,
Yanni Hu  and
Yiying Zhang
Peng Zhao
Affiliation:
School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, China E-mail: zhaop@jsnu.edu.cn
Yanni Hu
Affiliation:
School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China
Yiying Zhang
Affiliation:
School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China
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Abstract

In this paper, we carry out stochastic comparisons of the largest order statistics arising from multiple-outlier gamma models with different both shape and scale parameters in the sense of various stochastic orderings including the likelihood ratio order, star order and dispersive order. It is proved, among others, that the weak majorization order between the scale parameter vectors along with the majorization order between the shape parameter vectors imply the likelihood ratio order between the largest order statistics. A quite general sufficient condition for the star order is presented. The new results established here strengthen and generalize some of the results known in the literature. Numerical examples and applications are also provided to explicate the theoretical results.

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Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 29 , Issue 4 , October 2015 , pp. 597 - 621
Copyright
Copyright © Cambridge University Press 2015 

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