The evaluation of trivariate normal probabilities defined by linear inequalities |
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Authors: | A J Hayter Y Lin |
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Institution: | 1. Department of Business Information and Analytics , University of Denver , Denver , CO , USA Anthony.Hayter@du.edu;3. Department of Statistics , The Chinese University of Hong Kong , Hong Kong |
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Abstract: | This paper considers the evaluation of probabilities which are defined by a set of linear inequalities of a trivariate normal distribution. It is shown that these probabilities can be evaluated by a one-dimensional numerical integration. The trivariate normal distribution can have any covariance matrix and any mean vector, and the probability can be defined by any number of one-sided and two-sided linear inequalities. This affords a practical and efficient method for the calculation of these probabilities which is superior to basic simulation methods. An application of this method to the analysis of pairwise comparisons of four treatment effects is discussed. |
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Keywords: | multivariate normal distribution trivariate normal distribution numerical integration recursive integration computational intensity linear inequality orthant probability pairwise comparisons |
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