  The shape of empirical distributions with heavy tails is a recurrent matter
of debate. There are claims of a power laws and the associated scale
invariance. There are plenty of challengers as well, the lognormal and
stretched exponential among others. Here I point out that, with regard to
summation invariance, all what matters is they are subexponential
distributions. I provide numerical examples highlighting the key properties of
subexponential distributions. The summation invariance and the black swan
dominance: the sum is dominated by the maximum. Finally, I illustrate the use
of these properties to tackle problems in random networks, infectious dynamics
and project delays.
