I am not sure how to put the question. I am not even sure if this question makes sense at all.
I know that the similarity of two discrete (or continuous) distributions can be quantified by Kullback–Leibler distance. However, I wonder if it makes sense to quantify the Kullback–Leibler distance between two random variables which one is discrete and the other one is continuous?
Is there any probabilistic measure for quantifying the similarity of continuos distribution with a discrete one.