Long tails in distributions are troublesome for 2 reasons:
- They are hard to test for empirically because they represent rare events. How they look like in any given model is more model-driven than data-driven.
- Models which are modular, and construct the distribution of interest from many independent component distributions, tend to underestimate long tails in the distribution of interest. This is a problem of degree, not a black and white issue – theoretical proofs use absolutely independent component distributions, and using those proofs for real work requires an assessment of whether components are independent enough in reality. That assessment is non-trivial and all too often skipped.