On the computation of the bivariate normal integral

  title={On the computation of the bivariate normal integral},
  author={Zvi Drezner and George O. Wesolowsky},
  journal={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. 

A simple approximation for the bivariate normal integral

Abstract A simple approximation for the bivariate normal cumulative distribution function based on the error function is derived. We compare the accuracy of our approximation with those of several

Approximations to the multivariate normal integral

We propose a simple and efficient way to approximate multivariate normal probabilities using univariate and bivariate probabilities. The approximation is computationally tested for the trivariate and

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Numerical Computation of Multivariate Normal Probabilities

  • A. Genz
  • Computer Science, Mathematics
  • 1992
This article describes a transformation that simplifies the problem and places it into a form that allows efficient calculation using standard numerical multiple integration algorithms.

Trapped by the Tails of the Bivariate Normal Distribution

Through the example of partial barrier options, we show that accuracy in the tail of the bivariate normal distribution is critical. We then propose a small change to a popular algorithm for the

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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.

The Bivariate Normal Copula

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Numerical computation of rectangular bivariate and trivariate normal and t probabilities

  • A. Genz
  • Mathematics, Computer Science
    Stat. Comput.
  • 2004
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.

An evaluation of the integral of the product of the error function and the normal probability density with application to the bivariate normal integral

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This error will only have an impact if one of the ranges of integration is so extreme that the marginal probability of the corresponding coordinate being in the range of integration is less than

Mathematical functions and their approximations