I've been fascinated to read the applications of the log-normal distribution.
My question:
By what heuristics do we decide to favor modeling a RV as a product of many independent RVs rather than the sum of many independent RVs?
For instance, human intelligence is often modeled by a normal distribution, but height and weight of humans is better viewed as log-normal. I have a feeling that this does not reflect the underlying genetics involved, but rather that we can invent our own units for IQ, so why not just invent ones where it's normal, not log-normal?
Possible heuristics:
- When we already have units for the RV (like in X = weight, but unlike X = intelligence), and those units are non-negative, then that points toward log-normal
- ?