Abstract
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.