Estimating joint probability density functions from marginals

By Mauricio N.A. Monsalve Moreno

Methodology

I created a methodology for estimating joint pdfs from marginal pdfs, which can be summarized in the following steps:
  1. Find functions S1..Sn such that each Yk = Sk(X1..Xk) forms a set of independent random variables.
  2. Estimate each gk, the pdf that Yk follows.
  3. The joint pdf of X1..Xn is simply:
    f(X1..Xn)=g1(Y1)..gn(Yn) dS1/dX1..dSn/dXn.
This methodology is further explained and proven in my paper.

Software: Joint PDF Estimator

I programmed an application for estimating joint pdfs from sample data. It only works when correlations are linear or almost linear. Note that I programmed it in Java using NetBeans (great for creating GUIs). How it looks
This is how Joint PDF Estimator looks like. It has a textarea which shows the joint pdf generated. From that explanation anyone should be able to write the joint pdf in an analytical form. (At least, this is what I believe!)

Datasets used

I used the following datasets to test my software (and my theory, in turn): I don't claim any kind of copyright over these datasets, even over these built by me.

For more datasets, go to:
Mauricio Monsalve, April 2009.