Multivariate normal distribution and multivariate order statistics induced by ordering linear combinations

In this paper, we consider n independent observations from a multivariate normal distribution and discuss the multivariate order statistics induced by ordering linear combinations of the components observed. Specifically, we derive means, variances and covariances of the induced multivariate order statistics; these quantities are expressed in terms of the means, variances and covariances of standard normal order statistics which have been tabulated quite extensively. These generalize the recent results of Song (1992) based on independent normal variables.