Authors

• Alireza Arabpour
• Mahsa Mahmood Molaiey
• Ahad Jamalizadeh

Abstract

In this paper, assuming that (X, Y1, Y2)T has a trivariate
normal distribution, we derive the exact joint distribution of (
X, Y(1),
Y(2))^T, where Y(1) and Y(2) are order statistics arising from (Y1, Y2)T .
We show that this joint distribution is a mixture of truncated trivariate
normal distributions and then use this mixture representation to derive
the best (nonlinear) predictiors of X in terms of (
Y(1), Y(2))^T. We also
predict Y(1) in terms of (
X, Y(2) )^T , and Y(2) in terms of (
X, Y(1))^T. Finally
illustrate the usefulness of these results by using real-life data.

Keywords

• Exchangeability
• linear and nonlinear predictors
• multivariate selection normal distribution
• multivariate unified skew-normal distribution
• Order statistics
• truncated trivariate normal distribution