Modelling income distributions based  on theoretical distributions derived  from normal distributions

Piotr Sulewski; Marcin Szymkowiak

doi:https://doi.org/10.59139/ws.2023.06.1

Modelling income distributions based on theoretical distributions derived from normal distributions

Piotr Sulewski Akademia Pomorska w Słupsku, Instytut Nauk Ścisłych i Technicznych, Polska / Pomeranian University in Słupsk, Institute of Exact and Technical Sciences, Poland. ORCID: https://orcid.org/0000-0002-0788-6567 , Marcin Szymkowiak Uniwersytet Ekonomiczny w Poznaniu, Instytut Informatyki i Ekonomii Ilościowej; Urząd Statystyczny w Poznaniu, Polska / Poznań University of Economics and Business, Institute of Informatics and Quantitative Economics; Statistical Office in Poznań, Poland. ORCID: https://orcid.org/0000-0003-3432-4364 Wiadomości Statystyczne. The Polish Statistician, vol. 68, 2023, 6, s. 1-23 Opublikowano online: 30 czerwca 2023 DOI https://doi.org/10.59139/ws.2023.06.1 Sposób cytowania: Sulewski, P., Szymkowiak, M. (2023). Modelling income distributions based on theoretical distributions derived from normal distributions. Wiadomości Statystyczne. The Polish Statistician, 68 (6), 1–23. https://doi.org/10.59139/ws.2023.06.1.

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ARTYKUŁ

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STRESZCZENIE

In income modelling studies, such well-known distributions as the Dagum, the lognormal or the Zenga distributions are often used as approximations of the observed distributions. The objective of the research described in the article is to verify the possibility of using other type of distributions, i.e. asymmetric distributions derived from normal distribution (ND) in the context of income modelling. Data from the 2011 EU-SILC survey on the monthly gross income per capita in Poland were used to assess the most important characteristics of the discussed distributions. The probability distributions were divided into two groups: I – distributions commonly used for income modelling (e.g. the Dagum distribution) and II – distributions derived from ND (e.g. the SU Johnson distribution). In addition to the visual evaluation of the usefulness of the analysed probability distributions, various numerical criteria were applied: information criteria for econometric models (such as the Akaike Information Criterion, Schwarz’s Bayesian Information Criterion and the Hannan-Quinn Information Criterion), measures of agreement, as well as empirical and theoretical characteristics, including a measure based on quantiles, specifically defined by the authors for the purposes of this article. The research found that the SU Johnson distribution (Group II), similarly to the Dagum distribution (Group I), can be successfully used for income modelling.

SŁOWA KLUCZOWE

income modelling, EU-SILC, normal distribution, SU Johnson distribution, Dagum distribution

JEL

C13, C15, C55, D31

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