kernel density estimation and regression (?)

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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

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