Moments of Order Statistics from the Equicorrelated Multivariate Normal Distribution

Owen, D. B.; Steck, G. P.

Ann. Math. Statist., Tome 33 (1962) no. 4, p. 1286-1291 / Harvested from Project Euclid

Résumé

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 $\rho = 0$.

Publié le : 1962-12-14
Classification:

@article{1177704361,
     author = {Owen, D. B. and Steck, G. P.},
     title = {Moments of Order Statistics from the Equicorrelated Multivariate Normal Distribution},
     journal = {Ann. Math. Statist.},
     volume = {33},
     number = {4},
     year = {1962},
     pages = { 1286-1291},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177704361}
}

Owen, D. B.; Steck, G. P. Moments of Order Statistics from the Equicorrelated Multivariate Normal Distribution. Ann. Math. Statist., Tome 33 (1962) no. 4, pp.  1286-1291. http://gdmltest.u-ga.fr/item/1177704361/