  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.
