Prediction in a trivariate normal distribution via a linear combination of order statistics

In this paper, by considering a trivariate normal distribution, we derive the exact joint distribution of one variable and a linear combination of order statistics from the other two variables. We show that this joint distribution is a mixture of unified bivariate skew-normal distributions. This mix...

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Bibliographic Details
Published in:Statistics & probability letters 2009-11, Vol.79 (21), p.2289-2296
Main Authors: Jamalizadeh, A., Balakrishnan, N.
Format: Article
Language:English
Subjects:
Exact sciences and technology
General topics
Inference from stochastic processes
time series analysis
Mathematics
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
Statistics
Stochastic processes
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Summary:In this paper, by considering a trivariate normal distribution, we derive the exact joint distribution of one variable and a linear combination of order statistics from the other two variables. We show that this joint distribution is a mixture of unified bivariate skew-normal distributions. This mixture form enables us to predict the variable based on a linear combination of order statistics from the other two variables. We finally illustrate the usefulness of these results by using a real-life data.
ISSN:0167-7152
1879-2103
DOI:10.1016/j.spl.2009.07.029