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.
Arabpour,A , Mahmood Molaiey,M and Jamalizadeh,A . (2022). Prediction in a Trivariate Normal Distribution via Two Order Statistics. Journal of the Iranian Statistical Society, 11(1), 39-56.
MLA
Arabpour,A , , Mahmood Molaiey,M , and Jamalizadeh,A . "Prediction in a Trivariate Normal Distribution via Two Order Statistics", Journal of the Iranian Statistical Society, 11, 1, 2022, 39-56.
HARVARD
Arabpour A, Mahmood Molaiey M, Jamalizadeh A. (2022). 'Prediction in a Trivariate Normal Distribution via Two Order Statistics', Journal of the Iranian Statistical Society, 11(1), pp. 39-56.
CHICAGO
A Arabpour, M Mahmood Molaiey and A Jamalizadeh, "Prediction in a Trivariate Normal Distribution via Two Order Statistics," Journal of the Iranian Statistical Society, 11 1 (2022): 39-56,
VANCOUVER
Arabpour A, Mahmood Molaiey M, Jamalizadeh A. Prediction in a Trivariate Normal Distribution via Two Order Statistics. JIRSS. 2022;11(1):39-56.
Journal of the Iranian Statistical Society