Three parameter beta distribution estimation procedure

Part of this. No procedure for a three parameter estimation can be found on Internet, so we have to come up with something.

The starting point is the four parameter Beta distribution found on wikipedia:

Form. 1.

This formula has two extra parameters a and c, which can be used to normalise the distribution to [0,1] with y = (c-a)x + a. As nutritional values always start at 0, we assume that a = 0. With this we can rewrite formula 1:

As MediaWiki does not supports maths (yet), have a look at this

A first experiment with estimating yielded no results: I did not manage to find the variables that converged to a solution. To be continued.