On the Statistical Properties and Tail Risk of Violent Conflicts

13 Pages Posted: 18 Oct 2015 Last revised: 27 Jun 2017

See all articles by Pasquale Cirillo

Pasquale Cirillo

Delft University of Technology; Delft University of Technology - Delft Institute of Applied Mathematics (DIAM)

Nassim Nicholas Taleb

New York University (NYU) - NYU Tandon School of Engineering

Date Written: October 16, 2015

Abstract

We examine statistical pictures of violent conflicts over the last 2000 years, finding techniques for dealing with incompleteness and unreliability of historical data.

We introduce a novel approach to apply extreme value theory to fat-tailed variables that have 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).

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 mean of war casualties, which proves to be considerably larger than the sample mean, meaning severe underestimation of the tail risks of conflicts from naive observation. We analyze the robustness of our results to errors in historical reports, taking into account the unreliability of accounts by historians and absence of critical data.

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.

Keywords: Risk, Extreme Value Theory, Black Swan, Violence

Suggested Citation

Cirillo, Pasquale and Taleb, Nassim Nicholas, On the Statistical Properties and Tail Risk of Violent Conflicts (October 16, 2015). Physica A., Forthcoming; NYU Tandon Research Paper No. 2675355. Available at SSRN: https://ssrn.com/abstract=2675355 or http://dx.doi.org/10.2139/ssrn.2675355

Pasquale Cirillo

Delft University of Technology ( email )

Stevinweg 1
Stevinweg 1
Delft, 2628 CN
Netherlands

Delft University of Technology - Delft Institute of Applied Mathematics (DIAM) ( email )

Mekelweg 4
Delft, Holland 2628
Netherlands

Nassim Nicholas Taleb (Contact Author)

New York University (NYU) - NYU Tandon School of Engineering ( email )

6 MetroTech Center
Brooklyn, NY 11201
United States

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