Moments of Order Statistics from the Equicorrelated Multivariate Normal Distribution

Abstract

Let $Z_1, Z_2, \cdots, Z_n$ be jointly normally distributed random variables with $EZ_i = 0, EZ^2_i = 1, EZ_iZ_j = \rho, i \neq j, -1/(n - 1) \leqq \rho \leqq 1$. Let the collection of random variables $\{Z_i\}$ be ordered so that $Z^{(1)} \geqq Z^{(2)} \geqq \cdots \geqq Z^{(n)}$. It is the purpose of this note to show how the moments and product moments of the $\{Z^{(i)}\}$ for any $\rho$ can be obtained from the corresponding moments and product moments of the $\{Z^{(i)}\}$ for $\rho = 0$.