Comparison of three-parameter models of income distribution in selected European countries

Kamila  Trzcińska; Małgorzata Ćwiek

doi:https://doi.org/10.59139/ws.2025.09.2

Kamila Trzcińska Uniwersytet Łódzki, Wydział Ekonomiczno-Socjologiczny, Instytut Statystyki i Demografii, Katedra Metod Statystycznych, Polska / University of Lodz, Faculty of Economics and Sociology, Institute of Statistics and Demography, Department of Statistical Methods, Poland ORCID: https://orcid.org/0000-0002-4714-4074 , Małgorzata Ćwiek Uniwersytet Ekonomiczny w Krakowie, Kolegium Ekonomii, Finansów i Prawa, Instytut Metod Ilościowych w Naukach Społecznych, Polska / Krakow University of Economics, College of Economics, Finance, and Law, Institute of Quantitative Methods in Social Sciences, Poland ORCID: https://orcid.org/0000-0002-6375-098X Wiadomości Statystyczne. The Polish Statistician, vol. 70, 2025, 9, s. 34-56 Opublikowano online: 30 września 2025 DOI https://doi.org/10.59139/ws.2025.09.2 Sposób cytowania: Trzcińska, K., Ćwiek, M. (2025). Comparison of three-parameter models of income distribution in selected European countries. Wiadomości Statystyczne. The Polish Statistician, 70(9), 34–56. https://doi.org/10.59139/ws.2025.09.2.

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ARTYKUŁ

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STRESZCZENIE

Income distribution modelling is a fundamental tool in economic analysis, providing insight into the structure of inequality and wealth in societies. Over the years, numerous models have been proposed to capture the complex nature of income distribution. The aim of the study presented in the article is to compare selected three-parameter income distribution models, i.e. the Singh-Maddala, the Dagum and the Zenga models, in terms of their goodness of fit to empirical data. The study covers six European countries, namely: France, Germany, Hungary, Czechia, Poland and Slovakia. The analyses, based on data for 2016 from the European Quality of Life Survey, were performed for the whole country and in a breakdown into big towns, small or middle-sized towns and rural areas (in total, 24 microdata sets). To compare the estimated theoretical distributions, two different measures of goodness of fit were used: the distribution similarity coefficient (W_p) and the Mortara index (A₁). The study also examined deviations of descriptive statistics based on theoretical distributions (median, mean, the first and the ninth decile) from empirical values.
The Zenga model best fitted the empirical data the greatest number of times, but the descriptive characteristics of income distribution estimated on the basis of the Dagum distribution deviated from empirical values to a much lesser degree. Moreover, the results indicate that even very high goodness of fit to empirical data, measured by the A₁ and W_p, does not guarantee that the descriptive characteristics calculated on the basis of theoretical distribution parameters would have the same values as the empirical ones.

SŁOWA KLUCZOWE

Dagum distribution, Singh-Maddala distribution, Zenga distribution, measures of goodness of fit

JEL

D31, C13, C15

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