Reverse engineer a new set of points from an original set by altering moments, skew, and/or Kurtosis?

I don't know if this is even possible but I'd like to be able to take a set of points, run something on them that calculates the mo开发者_C百科ments, skew and kurtosis values, and have another function that would take those elements and reverse engineer a new set of points using modified values for the moments, skew and/or kurtosis. I already have the analytical function in Delphi Pro 6 which is:

procedure MomentSkewKurtosis(const Data: array of Double;var M1, M2, M3, M4, Skew,Kurtosis: Extended);

I'm looking for a partner function that could return a new Data array after I make alterations to any of the output parameters "var" in MomentSkewKurtosis() and pass them back in to the partner function as input parameters. For example, suppose I wanted to increase the Skew of the data and get a new set of points back that would be the original set of points altered just enough to generate the new Skew value.

The problem is not easy, and probably better targetted at stats, but I'll give you a pointer to a paper that I think is very good, and straight to the mark: Towards the Optimal Reconstruction of a Distribution from its Moments

Hope this helps!

Obviously you can't reconstruct an arbitrary density distribution from a finite amount of variables. You can create a distribution which fits the parameters, but it's not necessarily the original distribution.

And as far as I remember Mean, Variance, Skew and Kurtosis are just functions of the first 4 momenta. So you can't choose them independently from the momenta.

On the other hand there exists a function which you can apply on each data member and that produces a new dataset with the desired properties. I suspect that since you fixed the first 4 momenta it's a polynomial of grade 3.