  The size that an epidemic can reach, measured in terms of the number of
fatalities, is an extremely relevant quantity. It has been recently claimed
[Cirillo & Taleb, Nature Physics 2020] that the size distribution of major
epidemics in human history is "extremely fat-tailed", i.e., asymptotically a
power law, which has important consequences for risk management. Reanalyzing
this data, we find that, although the fatality distribution may be compatible
with a power-law tail, these results are not conclusive, and other
distributions, not fat-tailed, could explain the data equally well. As an
example, simulation of a log-normally distributed random variable provides
synthetic data whose statistics are undistinguishable from the statistics of
the empirical data. Theoretical reasons justifying a power-law tail as well as
limitations in the current data are also discussed.
