流行病死亡人数分布的尾部
Tail of the distribution of fatalities in epidemics
摘要：
以死亡人数衡量，一种流行病可能达到的规模是一个极为相关的数量。最近有人声称[Cirillo & Taleb，Nature Physics 2020]，人类历史上主要流行病的规模分布是“极端肥尾”的，即，渐近幂律，这对风险管理有重要影响。重新分析这些数据，我们发现，虽然死亡率分布可能与幂律尾兼容，但这些结果并不是决定性的，其他分布，而不是厚尾，可以同样很好地解释数据。作为示例，对数正态分布随机变量的模拟提供了其统计与经验数据的统计不可区分的合成数据。理论上的原因证明幂律尾以及在目前的数据的局限性进行了讨论。
英文摘要：
The size that an epidemic can reach, measured in terms of the number of fatalities, is an extremely relevant quantity. It has been recently claimed [Cirillo & Taleb, Nature Physics 2020] that the size distribution of major epidemics in human history is "extremely fat-tailed", i.e., asymptotically a power law, which has important consequences for risk management. Reanalyzing this data, we find that, although the fatality distribution may be compatible with a power-law tail, these results are not conclusive, and other distributions, not fat-tailed, could explain the data equally well. As an example, simulation of a log-normally distributed random variable provides synthetic data whose statistics are undistinguishable from the statistics of the empirical data. Theoretical reasons justifying a power-law tail as well as limitations in the current data are also discussed.
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