An identity on order statistics of a set of random variables.

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.