A Simple Approximation for Bivariate Normal Probabilities

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Abstract
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 [–0.5, 0.5], the maximum absolute error in our approximation is always less than 0.0008. The conditional distribution that we approximate is referred to as a ‘normal conditioned on a truncated normal’ distribution and is related to screening problems.