4 ms·
Takes a lot of samples to converge to the mean of a fat tailed distribution.
by greesil 6y ago
Takes a lot of samples to converge to the mean of a fat tailed distribution.
- zeroer 6y agoIf ever. The Central Limit Theorem requires the distribution to have finite standard deviation.
- arthurcolle 6y agoyou should read Taleb's new book "Statistical Consequences of Fat Tails"
- spekcular 6y agoI realize this is a bit off topic, but no, the parent poster should not. It's a mish-mash of poorly explained introductory probability material. There are numerous other textbooks on statistical aspects of heavy-tailed random variables that would be far more insightful.
- dannyw 6y agoTaleb is a great writer, but not a great teacher.
- arthurcolle 6y agoI enjoyed it, but I can see why someone might get that impression. Care to share other reads?
- spekcular 6y agoDidier Sornette, Critical Phenomena in Natural Sciences: Chaos, Fractals, Selforganization and Disorder. Springer, 2nd edition. This covers the mathematics of heavy-tailed distributions and a lot of fun applications, and also touches on some other interesting, Taleb-esque topics (fractals, renormalization group). For financial stuff in this vein (heavy tails), Bouchaud has some books with various coauthors (e.g. Theory of Financial Risk and Derivative Pricing: From Statistical Physics to Risk Management). Admittedly I have only browsed them, but what little I've read has been good. Also, on a tangent which may interest you, Charles Martin and Mike Mahoney (of UC Berkeley) have some recent work which uncovers heavy-tailed laws in neural networks. You can get started here and follow the citations: https://arxiv.org/abs/1901.08278 https://arxiv.org/abs/1901.08278.