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On the Computation of Integrals of Bivariate Gaussian Distribution

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posted on 21.02.2020 by Vincent 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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Email Address of Submitting Author

vincent.savaux@b-com.com

ORCID of Submitting Author

0000000234834869

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b<>com

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France

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