# Compute moments of aggregate loss using Monte Carlo

Spin-off from here.

Richard referred to me an article that tells me how to get parameters of a translated gamma distribution to which I should consider fitting simulated aggregated loss values.

The parameters depend on moments of S (or. in Richard's terms, L):

How do I compute the $E(S), E(S^2) and E(S^3)$ given simulations of S?

Do I estimate them with mean(S), mean(S^2) and mean(S^3), or do I use the formulas given in the article?

I wouldn't know how to compute the $E(S^3)$ ...

as you post 3 questions on this topic and after reading them: this is homerwork/study material- right? So for comparing Fast Fourier, MC and Panjer there are tons of publications out there. For the formulas for the momemts of $S$ look here or google "moments in the collective risk model". You should notice that:
• If you know the distribution of $N$ and $X$ then you know the moments and using those formulas you can calculate the moments of $S$ without MC. Just plug in.