A useful family of fat-tailed distributions

TL;DR

This paper introduces a new three-parameter fat-tailed distribution that resembles the t-distribution but has finite moments and a well-defined moment-generating function, useful for robustness analysis and financial computations.

Contribution

A novel three-parameter distribution that interpolates between normal and Cauchy, with finite moments and practical algorithms, expanding the toolkit for statistical modeling.

Findings

Distribution visually resembles t-distribution

Has all moments finite and a moment-generating function

Includes algorithms for random-number generation

Abstract

It is argued that there is a need for fat-tailed distributions that become thin in the extreme tail. A 3-parameter distribution is introduced that visually resembles the t-distribution and interpolates between the normal distribution and the Cauchy distribution. It is fat-tailed, but has all moments finite, and the moment-generating function exists. It would be useful as an alternative to the t-distribution for a sensitivity analysis to check the robustness of results or for computations where finite moments are needed, such as in option-pricing. It can be motivated probabilistically in at least two ways, either as the random thinning of a long-tailed distribution, or as random variation of the variance of a normal distribution. Its properties are described, algorithms for random-number generation are provided, and examples of its use in data-fitting given. Some related distributions are also discussed, including asymmetric and multivariate distributions.