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My introduction to the central limit theorem was that chained independent random processes tend to result in a Gaussian distribution. This is so general that o
by jhallenworld 12y ago
My introduction to the central limit theorem was that chained independent random processes tend to result in a Gaussian distribution. This is so general that one is surprised when one finds non-Gaussian distributions (canonical example: the stock market).
I attended a lecture by Mandelbrot (shortly before he died) where he spoke at length about this- take a look at stable distributions and the generalized central limit theorem.
- dnautics 12y agoI think that Mandelbrot's point is actually quite the opposite - that non-gaussian stable distributions are the norm; and that we are trained to see gaussians and that's why we're surprised. When alpha is very close to 2 (e.g. 1.9 and above it really makes little difference) but even a bit lower like 1.8 you can have some very scary consequences for modelling. In his book he has an example of an insurance market and modelling the failure of insurance companies... Which was especially poignant considering what happened after he died (and what is happening now).