Pareto versus lognormal: a maximum entropy test

It is commonly found that distributions that seem to be lognormal over a broad range change to a power-law (Pareto) distribution for the last few percentiles. The distributions of species abundance, income and wealth as well as file, city and firm sizes are examples with this structure. We present a new test for the occurrence of power-law tails in statistical distributions based on maximum entropy. This methodology allows to identify the true data generating processes even in the case when it is neither lognormal nor Pareto. The maximum entropy approach is then compared with alternative methods at different levels of aggregation of economic systems. Our results provide support to the theory that distributions with lognormal body and Pareto tail can be generated as mixtures of lognormally distributed units.