How do I generate random nos based on say k moments? (no other constraints on support) When k = 2, we generate random nos. from a normal distribution defined by the 2 moments. Can we generalize this idea to an arbitrary k.
A related question: Is normal distribution the only (known) distribution which is defined by just 1st 2 moments?
I wouldn't mind suggestions for books/links, instead of direct answers to these questions.
(Editing the question based on a couple of answers I got)
I'll try to provide the context in which I thought of this question. I have a uni variate sample and no more information about anything. Now, I want to try and simulate nos. from the distribution from which this sample was drawn. I could just find its 1st 2 moments, assume this sample to be normally distributed, and be done. But if I want do away with 'Normal' assumption, I can try to find it's first k moments and somehow draw from the distribution defined by these k moments.
I am interested in its theoretical underpinnings as well as practical implementation.