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DISPERSIVE ORDERING FOR THE MULTIVARIATE NORMAL DISTRIBUTION

Published online by Cambridge University Press:  05 January 2016

Xuan Leng ,
Jinsen Zhuang  and
Taizhong Hu
Xuan Leng
Affiliation:
Department of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei, Anhui 230026, China E-mail: lxuan10@mail.ustc.edu.cn
Jinsen Zhuang
Affiliation:
Department of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei, Anhui 230026, China E-mail: zzjinsen@ustc.edu.cn
Taizhong Hu
Affiliation:
Department of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei, Anhui 230026, China E-mail: thu@ustc.edu.cn
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Abstract

Let (X1, …, Xn) be a multivariate normal random vector with any mean vector, variances equal to 1 and covariances equal and positive. Turner and Whitehead [9] established that the largest order statistic max{X1, …, Xn} is less than the standard normal random variable in the dispersive order. In this paper, we give a new and straightforward proof for this result. Several possible extensions of this result are also discussed.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 30 , Issue 2 , April 2016 , pp. 141 - 152
Copyright
Copyright © Cambridge University Press 2016 

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References

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