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On the Computation of Integrals of Bivariate Gaussian Distribution
  • Vincent Savaux ,
  • Luc Le Magoarou
Vincent Savaux

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Luc Le Magoarou
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This paper deals with the computation of integrals
of centred bivariate Gaussian densities over any domain defined as an angular sector of R^2. Based on an accessible geometrical approach of the problem, we suggest to transform the double integral into a single one, leading to a tractable closed-form expression only involving trigonometric functions. This solution can also be seen as the angular cumulative distribution of bivariate centered Gaussian variables (X,Y). We aim to provide a didactic approach of our results, and we validate them by comparing with those of the literature.