Sociophysics of income distributions modeled by deformed fermi-dirac distributions

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 $${\chi ^2}$$χ2 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 $${r^2}$$r2 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 $${r^2}$$r2 values are correlated with the Gini index for those of considered systems.