Hey all,

I'm working with a set of stochastic differential equations for which I've analytically solved for the steady state of the first 4-5 moments. I've done this because solving for the complete distribution of the discrete probability mass function (numerically) is incredibly computationally slow.

I also have data that I'm trying to 'fit' based on the moments. One thing I'm interested in is what a distribution looks like given the first 5 moments. I've gathered from extensive internet searching that it's possible to derive the distribution from its moments because there is a unique mapping of one to the other (given ALL of the moments). However, I've not come across a clear explanation of how to approximate the PMF given a finite set of the moments. Suggestions?