Computation of the Bi-Variate Normal Integral

SUMMARY This paper is concerned with the problem of calculating the bi-variate normal integral, with particular reference to the need for a procedure suitable for general computer application. Three methods which involve the reduction of the general twofold integral to a form which is effectively a single integral are considered. The methods are compared on the basis of the computing time required for a given accuracy of approximation and it is shown that the most suitable alternative in a given case can be determined mainly upon the basis of the correlation coefficient. A computing procedure involving the use of the most appropriate method of reduction in a particular case is put forward.