Statistical Consequences of Fat Tails: Real World Preasymptotics, Epistemology, and Applications

Understand

(The third edition corrects minor typos and adds 3 chapters synthesized from published papers plus an appendix on maximum entropy distributions.) The monograph investigates the misapplication of conventional statistical techniques to fat tailed distributions and looks for remedies, when possible.

• Switching from thin tailed to fat tailed distributions requires more than "changing the color of the dress".
• Traditional asymptotics deal mainly with either n=1 or $n=\infty$, and the real world is in between, under of the "laws of the medium numbers" --which vary widely across specific distributions.
• Both the law of large numbers and the generalized central limit mechanisms operate in highly idiosyncratic ways outside the standard Gaussian or Levy-Stable basins of convergence.