Approximation of certain multivariate integrals

A Taylor series approximation to multivariate integrals taken with respect to a multivariate probability distribution is proposed and applied to the computation of multivariate normal probabilities and conditional expectations. The approximation does not require that the multivariate distribution have a structured covariance matrix and, in its simplest form, can be written as the product of univariate integrals. The approximation is compared to that of Mendell and Elston (1974) for computing bivariate normal probabilities.