On the computation of the bivariate normal integral

@article{Drezner1990OnTC,
  title={On the computation of the bivariate normal integral},
  author={Z. Drezner and G. O. Wesolowsky},
  journal={Journal of Statistical Computation and Simulation},
  year={1990},
  volume={35},
  pages={101-107}
}
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. 
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  • Mathematics, Computer Science
  • Stat. Comput.
  • 2004
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Test results are provided, along with recommendations for the most efficient algorithms for single and double precision computations, and a generalization of Plackett's formula is derived for bivariate and trivariate t probabilities. Expand
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References

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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… Expand
On computation of the bivariate normal distribution
A quadrature and two series representations are given as limiting cases of a bivariate t-distribution. The quadrature is taken over the complementary error function and the series are sums of Bessel… Expand
Tables for Computing Bivariate Normal Probabilities
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Abstract: About a decade ago, biophysicists observed an approximately linear relationship between the combinatorial complexity of knotted DNA and the distance traveled in gel electrophoresis… Expand
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