Journal of Statistical Theory and Practice

, Volume 5, Issue 4, pp 563–589 | Cite as

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

  • A. J. HayterEmail author


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.

AMS Subject Classification



Multivariate normal distribution Recursive integration Numerical integration Computational intensity Tree structure Tri-diagonal matrix Orthant probability 


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Copyright information

© Grace Scientific Publishing 2011

Authors and Affiliations

  1. 1.Department of Business Information and AnalyticsUniversity of DenverDenverUSA

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