So I can generate
X from arbitrary CDF F(x) by the procedure above. Can it be generalized to two variables? How, exactly? If not, what's the best way to generate
(X,Y) from arbitrary CDF F(x,y) or PDF f(x,y)?
I am no expert in the field but I can imagine 3 different cases :
- Variables are independent in which case you can use your formula on each
- You have access to some chain rules decomposition that allows you to easily generate each variable one at a time using your formula
- If none of the above : https://appsilon.com/how-to-sample-from-multidimensional-distributions-using-gibbs-sampling/