> 30,000 times more initial energy than any recorded events As a statistician: this is why heavy-tailed modeling matters. Schools teach the finite-variance version of the Central Limit Theorem and students believe they live in a normal world. The real Central Limit Theorem [1] predicts large rare events following Lévy α-stable distributions. [1] https://en.wikipedia.org/wiki/Stable_distribution#A_generali...
I'm no expert on stats, this discussion is a bit over my head, but it reminds me that not all distributions have a mean. A Cauchy distribution has no mean; as you average successive samples, it never settles down to a consistent average. I was surprised when I first encountered Cauchy distributions and up until then had considered that all distributions would have a mean. I suppose it is one of those "heavy-tailed" d…
How much water does your faucet leak per day? That might be a good case for a normal distribution. But today I smack it with a hammer and it can’t stop flowing. We now have a ton of water far more than should ever appear on that original normal distribution. Is that because the model is wrong? No. It’s because the model is not designed for these circumstances.
We can’t build a model that estimates flow distribution including the possibility that I smack it with a hammer. That doesn’t mean we don’t believe it won’t ever happen or even that we think it is unlikely to happen. It’s just a weird edge case.
A lot of people (taleb) imply statisticians are idiots because they insist the distributions are comprehensive. But statisticians don’t insist this. Black swan, fat tails, and all that are just terms for things outside modeled conditions. And yeah. They happen.