Finite-size scaling versus dual random variables and shadow moments in the size distribution of epidemics

I discuss and criticize the use of "dual transformations" to calculate "shadow moments" in the distribution of epidemic fatalities. I show how this transformation is arbitrary and not only yields an unjustified functional form for the distribution of fatalities but turns out to be highly unphysical (see Fig. 1 in the manuscript). Therefore, the expected number of fatalities calculated from the "shadow moments" approach lacks any theoretical support. This is of fundamental importance to assess risk from pandemics. I argue that the natural way to address this sort of problems in statistical physics is by means of finite-size scaling.