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At the end of 19th century Vilfredo Pareto, as the first tried by using power-laws to describe wealth and income distributions in society. We applied early works of Pareto as well as Gibrat (i.e. laws of Pareto and rules of proportionate growth, respectively). Furthermore, we used recent and advanced models: the Generalised Lotka-Volterra model and collision models. By using empirical data for annual income of Polish households, e.g. for years 2003 and 2006, the comparison with these theoretical models was successfully made. The surprisingly good agreements with Pareto distribution were obtained, where Pareto exponents near the cubic law were found for middle class. For the low class very good agreement with prediction of the cumulative log-normal distribution was gained. Hence, it was possible to establish the border between low and middle society levels. The same was possible for the border between high and middle classes as the ranking for the former follows (to some extent) the Zipf law.

Study of Households' Income in Poland by Using the Statistical Physics Approach