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Different population behaviours could be modeled via multi-level models.


They can, but you start running into problems with the mathematical formulation of your model. For example, Weibull's CF doesn't have a closed form, which means it's hard to find convolutions even with itself, so that finding e.g. the sum of Weibull distributed r.v. is hard, even if they are iid.

Again, modeling done right is super hard.




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