Sociophysics of Income Distributions Modeled by Deformed Fermi-Dirac Distributions

Abstract

In order to model the income data, the physical distributions of Fermi-Dirac and Bose-Einstein families have already been proposed in the literature. In this study, we generalize Fermi-Dirac distribution by using a q,p-deformed version of Fermi-Dirac distribution which provides the advantage of working with flexible free q, p deformation parameters as the regression parameters for modeling the income data. We analyze the accuracy of the generalized version, q,p-deformed Fermi-Dirac distribution, on describing the data of income share held by quintiles for countries, and household income for the states of U.S.A. in 2018. We also use chi(2) minimization routine for modeling the data which leads to the best fit parameters for the deformation parameters q and p. Subsequently, we plot the fitted q, p-deformed Fermi-Dirac distribution as income distribution with the obtained deformation parameters, then find the statistical confidence values r(2) from the fitted curve. We figure out that our model properly describes the income data for the systems experiencing a high level of income inequality, and also r(2) values are correlated with the Gini index for those of considered systems.