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
Pareto distributions, and power laws in general, have demonstrated to be very useful models to describe very different phenomena, from physics to finance. In recent years, the econophysical literature has proposed a large amount of papers and models justifying the presence of power laws in economic data. Most of the times, this Paretianity is inferred from the observation of some plots, such as the Zipf plot and the mean excess plot. If the Zipf plot looks almost linear, then everything is ok and the parameters of the Pareto distribution are estimated. Often with OLS. Unfortunately, as we show in this paper, these heuristic graphical tools are not reliable. To be more exact, we show that only a combination of plots can give some degree of confidence about the real presence of Paretianity in the data. We start by reviewing some of the most important plots, discussing their points of strength and weakness, and then we propose some additional tools that can be used to refine the analysis.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.