How to approximate a probability density function using its moments?

Question

I have an unknown probability density function(pdf) with support on the real line and I can compute numerically all its moments. How can I then approximate this pdf using any technique/algorithm?

I have read that this problem is sometimes called the 'Hamburger moment problem' and that Laplace transforms could help.

Thanks! Maria

Answer 1

A good approximation is the set of Pearson distributions. They allow you to include information of both kurtosis and skewness. Moreover, you can use them even when the support is not the whole real line