Metrics for Mass-Count Disparity

Mass-count disparity is the technical underpinning of the "mice and elephants" phenomenon - that most samples are small, but a few are huge - which may be the most important attribute of heavy-tailed distributions. We propose to visualize this phenomenon by plotting the conventional distribution and the mass distribution together in the same plot. This then leads to a natural quantification of the effect based on the distance between the two distributions. Such a quantification addresses this important phenomenon directly, taking the full distribution into account, rather than focusing on the mathematical properties of the tail of the distribution. In particular, it shows that the Pareto distribution with tail index 1 le a le 2 actually has a relatively low mass-count disparity; the effects often observed are the result of combining some other distribution with a Pareto tail.