Optimal income crossover for a two-class model using particle swarm optimization.

Personal income distribution may exhibit a two-class structure, such that the lower income class of the population (85-98%) is described by exponential Boltzmann-Gibbs distribution, whereas the upper income class (2-15%) has a Pareto power-law distribution. We propose a method, based on a theoretical and numerical optimization scheme, which allows us to determine the crossover income between the distributions, the temperature of the Boltzmann-Gibbs distribution, and the Pareto index. Using this method, the Brazilian income distribution data provided by the National Household Sample Survey was studied.