I know first $N$ moments of some distribution. I also know that my distribution is continuous, unimodal and well shaped (it looks like gamma-distribution). Is it possible to:
Using some algorithm, generate samples from this distribution, which in limit conditions will have exactly the same moments?
Solve this problem analytically?
I understand that until I have an infinite number of moments, this question cannot have a unique solution. I would be happy to have any.
Due to the comments clarification: I don't need to restore original distribution. I need ANY with a given moments.