There’s no need to get mathy tbh. Distributions are not real, and the ones we create only describe parts of what actually happens. This is obvious and always ha

There’s no need to get mathy tbh. Distributions are not real, and the ones we create only describe parts of what actually happens. This is obvious and always has been. 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.