What is the general formula for the skewness of S? where S is the aggregate claim amounts. I know the Skewness of S is lambda*E[X^3] if N follows a Poisson distribution with parameter lambda.
To find the skewness of S in the case where N is not Poisson, you would have to work from first principles, using the MGF. It's a bit of a bore. By an astonishing coincidence however, I happen to have the derivation for a compound negative binomial distribution to hand (see attached). A similar method can be used for any other discrete distribution.
