CubeRootOfTrue@skewray True!
1/f distributions --- one of my advisors told me not to study that because it would destroy my career. His name was Per Bak. I ignored him. He was right tho
Lévy distributions are a nice example of a convolutionally stable power law with non-Gaussian behavior. Cauchy distributions, despite having no finite mean or variance are also stable. α-stable.
You do need infinite data to know the true asymptotic shape of a distribution ...
It is possible to measure the fatness of the tails of a distribution ... But I've been told that "α-stable laws are both beautiful and frustrating: they’re mathematically neat, but empirically very hard to confirm.", so yeah, what Bak said