On an independent result using order statistics and their concomitant

Document Type : Research Paper

Author

Department of Statistics, Faculty of mathematics and computer, Shahid Bahonar university of Kerman, Kerman, Iran

Abstract

Let

X_{1}, X_{2}, . . ., X_{n}

have a jointly multivariate exchangeable normal distribution. In this work we investigate another proof of the independence of

X

and

S^{2}

using order statistics. We also assume that

(X_{i}, Y_{i}), i = 1, 2, . . ., n,

jointly distributed in bivariate normal and establish the independence of the mean and the variance of concomitants of order statistics.

Keywords