Volume 11, Number 1 (2012) | JIRSS 2012, 11(1): 39-56 | Back to browse issues page


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Arabpour A, Mahmood Molaiey M, Jamalizadeh A. Prediction in a Trivariate Normal Distribution via Two Order Statistics. JIRSS. 2012; 11 (1) :39-56
URL: http://jirss.irstat.ir/article-1-174-en.html

Abstract:   (7807 Views)
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.
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Subject: 60: Probability theory and stochastic processes
Received: 2012/03/3 | Accepted: 2015/09/12

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