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Aug 18, 2021 at 11:32 vote accept DM-97
Aug 18, 2021 at 11:32 comment added DM-97 Thanks. I ran some more simulations to test a few different distributions for $X_i$ and functions $f$, and found approximately the right mean, variance, skew (0) and kurtosis (3) most of the time. The approximation is poor for lognormal $X_i$ unless (presumably) $n$ is larger than I'm patient enough to simulate. But that's not too surprising as it's heavy-tailed.
Aug 16, 2021 at 23:48 history answered Geoffrey Johnson CC BY-SA 4.0