## The Annals of Mathematical Statistics

### 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 $\rho = 0$.

#### Article information

Source
Ann. Math. Statist., Volume 33, Number 4 (1962), 1286-1291.

Dates
First available in Project Euclid: 27 April 2007

https://projecteuclid.org/euclid.aoms/1177704361

Digital Object Identifier
doi:10.1214/aoms/1177704361

Mathematical Reviews number (MathSciNet)
MR141178

Zentralblatt MATH identifier
0107.36302

JSTOR