The Fermi–Dirac distribution modeling of income distribution of developing and developed countries: A comparative study of Indonesia, United States, and Singapore

The distribution of income constitutes a fundamental indicator of economic development, forming the empirical basis for assessing inequality through quantitative measures such as the Gini coefficient. As a contribution to the field of econophysics, this study develops an analytical model of income distribution for the Lorenz curve — a mathematical representation of income inequality — based on the Fermi–Dirac (FD) distribution. The purposes of this research are: proving the analogy between household income distribution and particle distribution using the thermodynamics-based and statistical mechanics-based approach, determining the fitness level of the FD distribution in modeling the income distribution, and visualizing the similar distribution behavior between the Lorenz curve and the FD Distribution. We performed comparative analyses along with household income data from countries with diverse economic characteristics, including the large-size developed country (USA), the small-size developed country (Singapore), and the large-size developing country (Indonesia), sourced from each country’s official statistics bureau. Note that the Indonesian household income dataset is proxied by household consumption expenditure, a common practice found in developing countries, raising its own intriguing question of whether the FD modeling would be robust under this proxy approach. The results then show that, regardless of the household income or expenditure data approach, the fitting model effectively fits the household income data within these countries. Through this work, we show that a direct modeling of Lorenz curve by the FD model is possible, and is to be further developed afterwards.