An error-bounded polynomial approximation for bivariate normal probabilities

Abstract

Although the bivariate normal distribution is frequently employed in the development of screening models, the formulae for computing bivariate normal probabilities are quite complicated. A simple and accurate error-bounded, noniterative approximation for bivariate normal probabilities based on a simple univariate normal quadratic or cubic approximation is developed for use in screening applications. The approximation, which is most accurate for large absolute correlation coefficients, is especially suitable for screening applications (e.g., in quality control), where large absolute correlations between performance and screening variables are desired. A special approximation for conditional bivariate normal probabilities is also provided which in quality control screening applications improves the accuracy of estimating the average outgoing product quality. Some anomalies in computing conditional bivariate normal probabilities using BNRDF and NORDF in IMSL are also discussed.