Anyone have ideas on the fastest way of getting the dimensions (number of coordinates) out of any Wolfram Language distribution. For some types (CategoricalDistributions) it is easy. And if a RandomVariate can be generated, it is easy too. But for symbolic distributions, one can't generate a random variate. One can try to compute a Mean or possibly a Median and get the number of coordinates in the response, but (a) that can sometimes be slow and (b) won't work on some distributions.

Why am I doing this? Trying to write a ResourceFunction provisionally titled NegativeCoordinateMarginalDistribution that would let you specify the coordinate with a negative value the same as you can specify a Part with a negative value. Useful if you want the last marginal of a distribution but aren't sure how many coordinates the distribution has.