I'm looking for a formula for computing the PDF (I would prefer the CDF if possible) of the product of two independent random variables.
I found the Mellin integral/transform is the analytical solution, but is there a practical/robust way to numerically compute this ?
In fact, my main preocupation is dealing with sums and products of independent random variables, so if there is any other method, I will appreciate too ; for example, I know that the Mellin transform of the product is the product of th eMellin transforms, and the characteristic function of the sum is the product of the characteristic functions, but with that I can not find the CDF of the sum of the product of two independent random variables ($Z = X\times Y + U\times V$ where $X,Y,U$ and $V$ are independent)