Fat Tails Quantified and Resolved: A New Distribution to Reveal and Characterize the Risk and Opportunity Inherent in Leptokurtic Data

Abstract

I report a new statistical distribution formulated to confront the infamous, long-standing, computational/modeling challenge presented by highly skewed and/or leptokurtic ("fat- or heavy-tailed") data. The distribution is straightforward, flexible and effective. Even when working with far fewer data points than are routinely required, it models non-Gaussian data samples, from peak center through far tails, within the context of a single probability density function (PDF) that is valid over an extremely broad range of dispersions and probability densities. The distribution is a precision tool to characterize the great risk and the great opportunity inherent in fat-tailed data.