Hi, So I can use the formulas Skew(S) =λE(X^3) and Coeff(S) = Skew(S)/(V(S)^1.5) if N is ~ Po(λ). What are the formulas when N is not ~ Poisson? I'm sure I've missed it but yeah I can't find it anywhere. I also tried Ask Jeeves but no luck.
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. Let me assure you, it's not much fun. By an astonishing coincidence however, I happen to have the derivation for a compound negative binomial distribution to hand. Please find this attached. Your formula for the coefficient of skewness is a general result, it can be used for any random variable.