Parameters estimation in a probabiility function

Hi,

I have a pdf function f(x,a), where x in {x1, x2} represents coordinates and a in {a1,a2} represents two parameters. By changing the parameters it´s possible to change the shape of the function. This function doesn't have any analytic form, so consider it numerical

I have furthermore 45 experimental data lets say xe={xe1,xe2} which can be described by a known pdf, let's say fe(xe,ae), where xe in {xe1, xe2} represents coordinates and ae in {ae1,ae2} represents two parameters. The parameters can be estimated by known methods.

I'm trying to find the following:

1. Item one an estimation of {a1,a2} based on the experimental data xe, and as a consequence f(x,a)
2. Item two comparison of f(x,a) with fe(xe,ae) and see the differences

I don't know where to start from. Could anybody give me some directions? Books, links etc are very welcome.