Suppose you have 3 two-dimensional gaussian distributions added up on each other pushed to be within 4 identical hyperbolas rotated in relation to each other by 90 degrees and their most proximal point to the zero point(origin of coordinate system) being identical in such a way that the limit of the boundaries(i.e. the hyperbolas) that push the gaussians are 0. (figuring out how would one "push" the Gaussians like this is an issue in and of itself, but what I'm trying to do is make all of the points further than the points of origin of the hyperbolas from the origin of the coordinate system be pushed to be within the boundary they outline on the side of the rest of the Gaussians in such a way that if one were to take the asymptotes of the hyperbolas and do a perpendicular intersection in the case there'd only be one Gaussian at the origin, the result would be another gaussian)
Slice and compare to each other the percentage(of the integral of the entire graph) of the intervals/sections(sort of as if I were to make a cookie-cutter by the shape of the two circles with lines formed by connecting the points of origin of the hyperbolas and comparing the amount of dough within each cookie-cutter hole) made by slicing it up into four quadrants from the zero point, then slicing up again by two circles, one that has a middle point at zero and kisses the most proximal points of the hyperbolas(i.e. the points of origin) and one that has the middle point the same as the first one but has half the radius, considering these slices and the complete area under the graph is equal to one, what is the area in each of the sections?
Is there a general solution for all possible modes(two-dimensional), means, skews, standard deviations.
I might be describing it poorly, but the top-down schematic should be something like this
