Heavy Tailed Distributions and the States of Randomness
I. Normality
The “Normal Distribution” (also called the Gaussian Distribution) is a very useful and well-studied tool for analysing data. It is however often misapplied, despite the efforts of Benoit Mandelbrot and Nassim Taleb to raise awareness of areas where it might be inappropriate to use. One reason people may be tempted to overuse it might be its name, which is a little too suggestive of it being some kind of “standard”, so henceforth I will use its alternative name to avoid perpetuating this any more than is inevitable.
The trouble is, that everyone is so familiar with the Gaussian Distribution, that it is very seductive to shoehorn your data into it and try to use the familiar techniques to analyse your data. When people see a “bell curve”, their first thought is usually “looks like it is Gaussian distributed”, meaning that the data behaves like it has been sampled from the graph below…
