How We Tend To Overestimate Powerlaw Tail Exponents

TL;DR

This paper explains why measurements often underestimate tail contributions in power-law distributions, attributing it to metaprobabilities that cause the asymptotic tail exponent to reflect the lowest possible value regardless of likelihood.

Contribution

It introduces a framework showing how uncertainty in parameters leads to systematic underestimation of tail exponents in power-law distributions.

Findings

Metaprobabilities influence tail exponent estimation.

Black Swan effects are explained by this framework.

Underestimation of tail risks is a systematic consequence.

Abstract

In the presence of a layer of metaprobabilities (from uncertainty concerning the parameters), the asymptotic tail exponent corresponds to the lowest possible tail exponent regardless of its probability. The problem explains "Black Swan" effects, i.e., why measurements tend to chronically underestimate tail contributions, rather than merely deliver imprecise but unbiased estimates.