kernel density estimation and regression (?)

Hello,

I am trying to estimate the pdf of a random variable two ways: First is by making an estimation analytically (by hand, calculus). The second is by using histograms and kernel density estimation.

Is it possible that I use the result from kernel density estimation in order to approximate or fit a continuous function based on what I have calculated by hand? Of course there are differences in the two techniques, but I would like to use the second as a 'benchmark' to be able to manipulate the first (perhaps by adding/multiplying constants).

I am not sure if this becomes a regression problem.

Thanks