Xu Jian-Lun
Biometry Research Group, National Cancer Institute, 9609 Medical Center Drive, Room 5E124, Bethesda, MD 20892-9789, USA.
J Multivar Anal. 2014 Aug 1;129:243-244. doi: 10.1016/j.jmva.2014.04.016.
When an × 1 random vector = (, …, ) has a sign-invariant distribution, Strait [J. Multivariate Anal. 4 (1974) 494-496] proved that the expectations of max(0, , + , …, + ) and max(0, , …, ) are equal. In this note we assume a weaker condition that (, , …, ) and (-, , …, ) are equal in distribution and prove a more general result that the expectations of (0, , + , …, + ) and (0, , …, ) are equal, where (0, , …, ) is the th order statistic of 0, , …, for = 1, …, + 1.
当一个(×1)随机向量(=(,\ldots,))具有符号不变分布时，斯特雷特[《多元分析杂志》4(1974)494 - 496]证明了(\max(0,, +,\ldots, +))和(\max(0,,\ldots,))的期望相等。在本注释中，我们假设一个较弱的条件，即((,,\ldots,))和(( -,,\ldots,))分布相等，并证明一个更一般的结果，即((0,, +,\ldots, +))和((0,,\ldots,))的期望相等，其中((0,,\ldots,))是(0,,\ldots,)对于( = 1,\ldots, + 1)的第( )阶统计量。
