This paper introduces in statistics the notion of the barycenter of the distribution of a non-negative random variable and explores its relation with the Gini index, the concentration area, and the Gini’s mean difference. The introduction of the barycenter allows for new economic, geometrical,...

This paper introduces in statistics the notion of the barycenter of the distribution of a non-negative random variable Y with a positive finite mean μY and the quantile function Q(x). The barycenter is denoted by μX and defined as the expected value of the random variable X having the...

A key aspect defining the contemporary income distribution is the (increasing) share the top holds compared to the rest. This paper shows that income concentration increases towards the very top of the distribution, while the shares the middle- and upper-middle-income groups hold remain stable...

The Household Integrated Economic Surveys (HIES) of the Pakistan Bureau of Statistics (PBS) reveal a low level of income inequality in Pakistan. However, this is due to large sampling and non-sampling errors. Appropriate adjustments for the size and inequality in income from different sources...

The cohesiveness of constituent nations in a confederation such as the Eurozone depends on their equally shared experiences. In terms of household incomes, commonality of distribution across those constituent nations with that of the Eurozone as an entity in itself is of the essence. Generally,...

This work studies trends in income distributions and inequality in the European Union using data from the European Union Statistics on Income and Living Conditions. We model the income distribution for each country under a Dagum distribution assumption and using maximum likelihood techniques. We...

Since globalisation accelerated in the early 1990s, income inequality has increased in most developed countries and in some middle-income countries, including China and India. Also, inequality has declined in most countries of Latin America and the Caribbean and in many Sub-Saharan African and...

In the machine learning community, the Gini index is a very popular score for model selection, and it is also used in actuarial science for evaluating insurance pricing models. The purpose of this tutorial is to discuss the Gini index, both its version in economics and its version in machine...

The evolution of Gini coefficient for personal incomes in the USA between 1947 and 2005 is analyzed and modeled. There are several versions of personal income distribution (PID) provided by the US Census Bureau (US CB) for this period with various levels of resolution. Effectively, these PIDs...

The Gini coefficient is based on the sum of pairwise income differences, which can be decomposed into separate sums for individuals. Differences vis-à-vis poorer people represent an individual’s advantage, while those with respect to richer people constitute deprivation. Weighting deprivation...