For distribution functions F and G we have the (Frechet) bounds:
max{0, F(x)+G(y) -1} = H(x,y) = min{F(x),F(y)}
where H is the joint df of (X,Y) having marginals F and G. If
X and Y are comonotonic (Schmeidler (Econometrica, 1989)), that is
if there is a random variable Z, such that X =
Dear Salvatore,
Assuming that you mean convolution when you write
additive linkage, the answer is that there is no general
answer. It will depend heavily on the joint distribution
of the two random variables.
Just to give a simple example, let X~f, Y~g, and
P(X=0.4)=P(Y=0.4)=1. Then, X and Y
