Assessment of goodness of fit of income distribution in France and Germany based on the Zenga distribution

Abstract

The aim of this paper is to apply the Zenga distribution for equivalent disposable income from the last two waves of European Quality of Life Surveys for Germany and France (both for total society and selected socio-economic groups) and to assess the goodness of fit to empirical data. The Zenga distribution has not been used to describe the income distribution in these countries yet. The obtained parameters were assessed for fitting to empirical data using two measures—the Wasserstein-Kantorovich and the Wasserstein-Kantorovich standardized measure. The analysis of the results received allows for the conclusion that the Zenga distribution can fit the income distributions both for small as well as large values. It was also shown that the Zenga distribution fits the data well even with small and very small samples. The article uses a new measure to assess the fit of the distribution to empirical data, based on the Wasserstein-Kantorovich measure assessing the distance between the empirical and theoretical cumulative distribution function. The modification consisted in standardizing the Wasserstein-Kantorovich measure by dividing the field between distributors by the rectangle area, where length is maximum income and width is maximum value of the cumulative distribution function. The proposed measure is not sensitive to extreme values, often found in the analysis of income distribution, and can be applied even in very small samples.