论文标题
量化意外：黑天鹅的科学方法
Quantifying the Unexpected: a scientific approach to Black Swans
论文作者
论文摘要
许多自然和社会经济系统的特征是幂律分布，使极端事件的发生不可忽略。这些事件有时被称为黑天鹅，但仍然缺乏对黑天鹅的定量定义。在这里，通过利用Zipf-Mandelbrot定律的属性，我们研究了这种极端事件与固有分布的上截止的动力学之间的关系。这种方法允许对极端事件进行量化，并允许将它们归类为白色，灰色或黑天鹅。我们的标准符合以前的一些发现，但也使我们能够发现黑天鹅的新例子，例如莱昂内尔·梅西（Lionel Messi）和土耳其航空公司981号航班灾难。我们开发的系统和定量方法允许对罕见事件进行科学而直接的分类，还提供了对黑天鹅背后的生成机制的新见解。
Many natural and socio-economic systems are characterized by power-law distributions that make the occurrence of extreme events not negligible. Such events are sometimes referred to as Black Swans, but a quantitative definition of a Black Swan is still lacking. Here, by leveraging on the properties of Zipf-Mandelbrot law, we investigate the relations between such extreme events and the dynamics of the upper cutoff of the inherent distribution. This approach permits a quantification of extreme events and allows to classify them as White, Grey, or Black Swans. Our criterion is in accordance with some previous findings, but also allows us to spot new examples of Black Swans, such as Lionel Messi and the Turkish Airline Flight 981 disaster. The systematic and quantitative methodology we developed allows a scientific and immediate categorization of rare events, providing also new insight into the generative mechanism behind Black Swans.
