A mechanism to derive multi-power law functions: An application in the econophysics framework

It is generally recognized that economical systems, and more in general complex systems, are characterized by power law distributions. Sometime, these distributions show a changing of the slope in the tail so that, more appropriately, they show a multi-power law behavior. We present a method to derive analytically a two-power law distribution starting from a single power law function recently obtained, in the frameworks of the generalized statistical mechanics based on the Sharma–Taneja–Mittal information measure. In order to test the method, we fit the cumulative distribution of personal income and gross domestic production of several countries, obtaining a good agreement for a wide range of data.