On moment based density approximations for aggregate losses

Jin et al. (2015) proposed a novel moments based approximation based on the gamma distribution for the compound sum of independent and identical random variables. They illustrated their approximation using six examples. Here, we revisit four of their examples. We show that moments based approximations based on simpler distributions can be good competitors. We also show that the moments based approximations are more accurate than truncated versions of the exact distribution of the compound sum.