I'm guessing that this is because sampling from arbitrary multi-dimensional distributions is generally not a simple problem which they haven't got around to implement yet. There are some trivial exceptions like ProbabilityDistribution[1, {x, 0, 1}, {y, 0, 1}]
, but in general it seems like you can only use build-in multi-dimensional distributions with RandomVariate
.
In your case, you could try to sample the unit disk by transforming the coordinates to r
and theta
. This will factorize the distribution so you can draw from two 1D distributions, which should be easy to do.