Extreme events and emergency scales

Veniamin Smirnov, Zhuanzhuan Ma, Dimitri Volchenkov

Research output: Contribution to journalReview articlepeer-review

3 Scopus citations


An event is extreme if its magnitude exceeds the threshold. A choice of a threshold is subject to uncertainty caused by a method, the size of available data, a hypothesis on statistics, etc. We assess the degree of uncertainty by the Shannon's entropy calculated on the probability that the threshold changes at any given time. If the amount of data is not sufficient, an observer is in the state of Lewis Carroll's Red Queen who said “When you say hill, I could show you hills, in comparison with which you'd call that a valley”. If we have enough data, the uncertainty curve peaks at two values clearly separating the magnitudes of events into three emergency scales: subcritical, critical, and extreme. Our approach to defining the emergency scale is validated by 39 years of Standard and Poor's 500 (S&P500) historical data.

Original languageEnglish
Article number105350
JournalCommunications in Nonlinear Science and Numerical Simulation
StatePublished - Nov 2020


  • Emergency scales
  • Extreme events
  • Uncertainty of threshold


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