Where Do Thin Tails Come From?

TL;DR

This paper explores how natural saturation effects in responses can transform initially fat-tailed distributions into thin-tailed ones, challenging traditional views on the origins of heavy tails.

Contribution

It introduces a general dose-response framework showing how bounded responses naturally lead to thin tails from fat-tailed sources.

Findings

Bounded responses induce thin tails from fat-tailed inputs.

Saturation effects explain the prevalence of thin tails in natural phenomena.

Inverse derivation offers new insights into tail behavior transformations.

Abstract

The literature of heavy tails (typically) starts with a random walk and finds mechanisms that lead to fat tails under aggregation. We follow the inverse route and show how starting with fat tails we get to thin-tails when deriving the probability distribution of the response to a random variable. We introduce a general dose-response curve and argue that the left and right-boundedness or saturation of the response in natural things leads to thin-tails, even when the "underlying" random variable at the source of the exposure is fat-tailed.