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

TL;DR

This paper introduces a new flexible statistical distribution designed to effectively model highly skewed and leptokurtic data, enabling better risk assessment and opportunity identification in fat-tailed datasets.

Contribution

A novel distribution that accurately models fat-tailed data with fewer data points, capturing the entire distribution from center to tails within a single PDF.

Findings

Models non-Gaussian data effectively

Valid over a broad range of dispersions

Enhances risk and opportunity analysis

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.