The numerical evaluation of a class of integrals. II

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Abstract
Consider the integral where x 1, x 2, …, xN are jointly distributed in a multivariate normal distribution f(x 1, x 2, …, xN ) with (pij ) as the correlation matrix. The integral has been expressed in an infinite series of tetrachoric functions for N≥2. The infinite series is not only complicated, but also is very slowly convergent and is consequently not of much practical use. Plackett (8) obtains a reduction formula for expressing normal integrals in four variates as a finite sum of single integrals of tabulated functions. These integrals have then to be evaluated by a rather awkward numerical quadrature.

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