The evaluation of two-sided orthant probabilities for a quadrivariate normal distribution

In this paper it is shown how a general two-sided orthant probability for a quadrivariate normal distribution can be evaluated by a one-dimensional numerical integral calculation. The quadrivariate normal distribution can have any covariance matrix and any mean vector. This affords a practical and efficient method for the calculation of these probabilities which is superior to simulation methods. The implementation of the algorithm is discussed, and some examples of its performance are provided. Copyright Springer-Verlag 2012