A really stimulating paper. Thank you. I particularly appreciate the recipe-like approach showing the method for obtaining the distribution!

Did you consider the (seemingly) simpler approach of calculating the skew (mean/median to keep it simpler) and having that number appear alongside any JIF? It would seem that a high skew would indicate the sort of 'lopsided' distribution that is worth noting. Advantages of this: it is easy to calculate, can be reported as a number (rather than a picture), and (because it is a number) can be computed and listed in tables such as your table 1. I have used the skew for this purpose myself.

An alternative would be to report the percentage of articles below the mean/JIF, which shows up several times in the text of the paper, suggesting that it communicates well exactly the phenomenon that is of concern.

On a related topic, at this spring's NAS Journal Summit, the issue of a mean being misleading for JIF calculations was raised (I could say "razed", since the debate was heated). A representative from Thomson Reuters indicated that it was not a mean but a ratio (between citations and citable items). Perhaps TR can explain if that matters for this proposed calculation of the distribution.