From subexponential distributions to black swan dominance

TL;DR

This paper clarifies that subexponential distributions, including power laws and lognormals, exhibit summation invariance where the maximum dominates the sum, impacting understanding of heavy-tailed phenomena in networks, epidemics, and delays.

Contribution

It emphasizes the importance of subexponentiality in heavy-tailed distributions and demonstrates their implications for black swan events across various fields.

Findings

Sum is dominated by the maximum in subexponential distributions

Numerical examples illustrate key properties of subexponential distributions

Applications to networks, epidemics, and project delays show practical relevance

Abstract

The shape of empirical distributions with heavy tails is a recurrent matter of debate. There are claims of a power laws and the associated scale invariance. There are plenty of challengers as well, the lognormal and stretched exponential among others. Here I point out that, with regard to summation invariance, all what matters is they are subexponential distributions. I provide numerical examples highlighting the key properties of subexponential distributions. The summation invariance and the black swan dominance: the sum is dominated by the maximum. Finally, I illustrate the use of these properties to tackle problems in random networks, infectious dynamics and project delays.