# On the computation of the bivariate normal integral

```@article{Drezner1990OnTC,
title={On the computation of the bivariate normal integral},
author={Zvi Drezner and George O. Wesolowsky},
journal={Journal of Statistical Computation and Simulation},
year={1990},
volume={35},
pages={101-107}
}```
• Published 1 March 1990
• Mathematics
• Journal of Statistical Computation and Simulation
We propose a simple and efficient way to calculate bivariate normal probabilities. The algorithm is based on a formula for the partial derivative of the bivariate probability with respect to the correlation coefficient.
216 Citations
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The new approximation method is compared with approximation methods based on products of univariate normal probabilities, using tests with random covariance-matrix/probability-region problems for up to twenty variables.
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This expression is beneficial, and can be used for evaluating the bivariate normal integral as a series expansion, a good alternative to the well-known tetrachoric series, when the correlation coefficient, ρ, is large in absolute value.