u003cbu003eThe book investigates the misapplication of conventional statistical techniques to fat tailed distributions and looks for remedies, when possible.u003c/bu003e 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=8, and the real world is in between, under 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. A few examples: - The sample mean is rarely in line with the population mean, with effect on "naïve empiricism," but can be sometimes be estimated via parametric methods. - The "empirical distribution" is rarely empirical. - Parameter uncertainty has compounding effects on statistical metrics. - Dimension reduction (principal components) fails. - Inequality estimators (Gini or quantile contributions) are not additive and produce wrong results. - Many "biases" found in psychology become entirely rational under more sophisticated probability distributions. - Most of the failures of financial economics, econometrics, and behavioral economics can be attributed to using the wrong distributions. u003cbu003eThis book, the first volume of the Technical Incerto, weaves a narrative around published journal articles.u003c/bu003e
