欠采样分布的矩：在流行病规模中的应用
Moments of undersampled distributions: Application to the size of epidemics
AI总结：
本文针对流行病总死亡人数的重尾统计问题，指出既有有界化变换的特设性，主张以统计物理有限尺寸标度处理，并说明核心困难是分布尾部欠采样而非均值不存在。
摘要：
一次流行病暴发造成的总死亡人数是一个沉重但极具信息量的量。了解这一量的统计规律，就能够计算在暴发已超过某一给定死亡人数的条件下，平均总死亡人数的大小，这对于风险评估十分重要。然而，总死亡人数似乎由幂律尾分布刻画，且其生存函数的指数小于1；由于这类分布不存在均值，这带来了一个重大理论困难。Cirillo和Taleb [Nature Phys. 16, 606 (2020)]提出了一种变换：从一个呈现幂律尾部的所谓对偶变量，变换到总死亡人数，并使后者受到世界总人口的限制。在本文中，我们：(i)表明这种变换是特设的且不符合物理；(ii)提出替代性的变换和分布（同样是特设的）；(iii)论证处理这一问题的正确框架是通过有限尺寸标度的统计物理；以及(iv)证明真正的问题并非幂律尾分布不存在均值，而是不同理论分布的尾部（这正是区分一个模型与另一个模型的关键）远未被现有数量的经验数据充分采样。我们的结果也适用于许多其他在规模上呈现（表观）幂律尾部的灾害。
英文摘要：
The total number of fatalities of an epidemic outbreak is a dramatic but extremely informative quantity. Knowledge of the statistics of this quantity allows the calculation of the mean total number of fatalities conditioned to the fact that the outbreak has surpassed a given number of fatalities, which is very relevant for risk assessment. However, the fact that the total number of fatalities seems to be characterized by a power-law tailed distribution with exponent (of the survival function) smaller than one poses an important theoretical difficulty, due to the non-existence of a mean value for such distributions. Cirillo and Taleb [Nature Phys. 16, 606 (2020)] propose a transformation from a so-called dual variable, which displays a power-law tail, to the total number of fatalities, which becomes bounded by the total world population. Here, we (i) show that such a transformation is ad hoc and unphysical; (ii) propose alternative transformations and distributions (also ad hoc); (iii) argue that the right framework for this problem is statistical physics, through finite-size scaling; and (iv) demonstrate that the real problem is not the non-existence of the mean value for power-law tailed distributions but the fact that the tail of the different theoretical distributions (which is what distinguishes one model from the other) is far from being well sampled with the available number of empirical data. Our results are also valid for many other hazards displaying (apparent) power-law tails in their size.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
