DISPERSIVE ORDERING FOR THE MULTIVARIATE NORMAL DISTRIBUTION

作者:Leng, Xuan*; Zhuang, Jinsen*; Hu, Taizhong*
来源:Probability in the Engineering and Informational Sciences, 2016, 30(2): 141-152.
DOI:10.1017/S0269964815000327

摘要

Let (X-1,...,X-n) 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{X-1,..., X-n} 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.

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