Quantifying the unexpected: A scientific approach to Black Swans

Many natural and socio-economic systems are characterized by power-law distributions that make the occurrence of extreme events not negligible. Such sometimes referred to as Black Swans, but a quantitative definition Swan is still lacking. Here, leveraging on properties Zipf-Mandelbrot law, we investigate relations between such dynamics upper cutoff inherent distribution. This approach permits quantification allows classify them White, Grey, or Swans. Our criterion in accordance with some previous findings, also us spot new examples Lionel Messi Turkish Airline Flight 981 disaster. The systematic methodology developed scientific immediate categorization rare events, providing insight into generative mechanism behind