A Simple Approximation for Bivariate Normal Probabilities

The bivariate normal distribution function may be expressed as the product of a marginal normal distribution times a conditional distribution. By approximating this conditional distribution, we obtain a simple method for approximating bivariate normal probabilities. When the correlation falls in the interval (-5, .5), the maximum absolute error in our approximation is always less than .0008. The conditional distribution that we approximate is referred to as a 'normal conditioned on a truncated normal' distribution and is related to screening and selection problems.