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On the Computation of Integrals of Bivariate Gaussian Distribution

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posted on 2020-02-21, 16:23 authored by Vincent SavauxVincent Savaux, Luc Le Magoarou
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.


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  • France