Suppose we have $X_{1} \sim B(m,p_{1}), X_{2} \sim B(m,p_{2}),\cdots, X_{n} \sim B(m,p_{n})$ and they are dependent. Does the joint distribution $f(X_{1},X_{2},\cdots,X_{n}) $ have a closed form?
Edit: let's take as an example a random graph, what's the joint distribution of the degrees of an ER random graph?
Best Answer
There is no unique joint distribution. In fact, there are infinite possibilities to construct the joint distribution. For instance, there exist infinitely many copula functions that can be used to construct a joint distributions with such marginals.