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I think the first half of the article showing how this works with a given sample distribution is pretty good. I don't think it's really doing much to build intu
by bkcooper 12y ago
I think the first half of the article showing how this works with a given sample distribution is pretty good. I don't think it's really doing much to build intuition at the end, though.
It's also worth pointing out that there are distributions for which the central limit theorem doesn't hold (e.g. the sum of samples from a Lorentzian distribution will again be Lorentzian, not Gaussian.)
- jordigh 12y ago> the sum of samples from a Lorentzian distribution will again be Lorentzian, not Gaussian Lorentzian? I had to look that up. Oh. Cauchy distribution. Right, because it doesn't have any finite moments, because the tails are too heavy.
- cozzyd 12y agoPhysicists like to say Lorentzian (or sometimes Breit-Wigner) instead of Cauchy.
- mturmon 12y agoI think the more typical case when the CLT is applied erroneously is not heavy tails, it's cases where the independence condition does not hold. Independence of an unbounded sequence of variables is a very strong assumption, but so easy to hide away with the magic letters, "iid".