On the statistical properties and tail risk of violent conflicts

P Cirillo, Nassim Nicholas Taleb

Research output: Contribution to journalArticleScientificpeer-review

42 Citations (Scopus)


We examine statistical pictures of violent conflicts over the last 2000 years, providing techniques for dealing with the unreliability of historical data.
We make use of a novel approach to deal with fat-tailed random variables with a remote but nonetheless finite upper bound, by defining a corresponding unbounded dual distribution (given that potential war casualties are bounded by the world population). This approach can also be applied to other fields of science where power laws play a role in modeling, like geology, hydrology, statistical physics and finance.
We apply methods from extreme value theory on the dual distribution and derive its tail properties. The dual method allows us to calculate the real tail mean of war casualties, which proves to be considerably larger than the corresponding sample mean for large thresholds, meaning severe underestimation of the tail risks of conflicts from naive observation. We analyze the robustness of our results to errors in historical reports.
We study inter-arrival times between tail events and find that no particular trend can be asserted.
All the statistical pictures obtained are at variance with the prevailing claims about “long peace”, namely that violence has been declining over time.
Original languageEnglish
Pages (from-to)29-45
Number of pages17
JournalPhysica A: Statistical Mechanics and its Applications
Publication statusPublished - 2016


  • Fat-tails
  • Power laws
  • Tail risk
  • Bounded support
  • War casualties
  • Infinite mean


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