Empirical nonextensive laws for the county distribution oftotal personal income and gross domestic product

Abstract

We analyze the cumulative distribution oftotal personal income ofUSA counties, and gross domestic product ofBrazilian, German and United Kingdom counties, and also ofworld countries.We verify that generalized exponential distributions, related to nonextensive statistical mechanics, describe almost the whole spectrum ofthe distributions (within acceptable errors), ranging from the low region to the middle region, and, in some cases, up to the power-law tail. The analysis over about 30 years (for USA and Brazil) shows a regular pattern of the parameters appearing in the present phenomenological approach, suggesting a possible connection between the underlying dynamics of(at least some aspects of) the economy ofa country (or ofthe whole world) and nonextensive statistical mechanics. We also introduce two additional examples related to geographical distributions: land areas ofcounties and land prices, and the same kind ofequations adjust the data in the whole range ofthe spectrum.