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Recursive Integration Methodologies with Applications to the Evaluation of Multivariate Normal Probabilities

This paper considers the evaluation of probabilities defined in terms of the multivariate normal distribution. The multivariate normal distribution can have any covariance matrix and any mean vector. Probabilities defined by a set of inequalities of linear combinations of the multivariate normal random variables are considered. It is shown how these probabilities can be evaluated from a series of one-dimensional integrations. This approach affords a practical algorithm for the evaluation of these probabilities which is considerably more efficient than more direct numerical integration approaches. Consequently, it enlarges the class of probabilities of this kind which are computationally feasible.