complex systems, social phenomena, statistics, inflection points, metalog distributions, Shannon entropy, Science, Astrophysics, QB460-466, Physics, QC1-999

Categorizing a population into different income classes is important for creating effective policies and analyzing markets. Our study develops a statistical method based on a nationwide survey of income distribution. We use these data to create a cumulative distribution function with a metalogistic distribution and its probability density function. We propose a new way to divide the population into income classes by using the inflection points of the probability density function as the class boundaries. As a case study, we apply this method to income data from Brazil between 2012 and 2022. We identify five income classes, with both their boundaries and the distribution of the population changing over time. To check our approach, we calculate the Gini coefficient and find that our results closely match official figures, with a root mean square deviation of less than 1%. By using individual income instead of family income, we avoid distortions caused by the fact that poorer families tend to be larger than wealthier ones. In the end, we identify five main income classes, with their boundaries shifting each year, reflecting the changing nature of income distribution in society.