A Probabilistic Model for the Distribution of GDP per Capita in NUTS 3 Zones of Europe

A macroeconomic indicator of productivity and economic development, used to obtain information on the economic and social conditions of a country, is the GDP per capita, which is also used as an indicator of social welfare. By construction it can be used directly to compare areas of interest. It is an indicator of great variability to which it is difficult to assign a probabilistic model to describe its distribution. In fact, it usually appears as a strongly asymmetric and frequently multimodal variable, which directly indicates a strong non-normality. In this work we propose to deal with the problem of finding a probabilistic model for this variable through the estimation of a model of finite mixtures of normal distributions. As an application example, we present the model obtained through the finite mixture for GDP per capita data from the NUTS 3 zones in the nomenclature of the European Union, EU countries and neighbouring countries. Thus, the model is estimated, its validity is checked and the results obtained are analysed, both for the GDP per capita variable and as a function of the countries to which the studied areas belong.