From subexponential distributions to black swan dominance

Alexei Vazquez

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arXiv · 2211.14069

From subexponential distributions to black swan dominance

Alexei Vazquez

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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.

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Alexei Vazquez. 2022-11-25. From subexponential distributions to black swan dominance. https://arxiv.org/abs/2211.14069

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