  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.
