I have two overlapping gamma distributions, 'a' and 'b', which are correlated but with correlation coefficient < 1. I want to randomly sample pairs of values, one from each distribution.
However, there is a physical relation between all sampled pairs such that 'a' must always be greater than 'b'. How can I enforce this condition without messing up the randomness/distribution of my samples?
[As noted, correlation coefficient = 1 would achieve this i.e. same P(X) used to sample from each distribution, but I don't want fully correlated samples]