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...

This paper defines and characterizes the concept of an increase in inverse downside inequality and show that, when the Lorenz curves of two income distributions intersect, how the change from one distribution to the other is judged by an inequality index exhibiting inverse downside inequality...

Much of the literature on inequality, both that on the theoretical features of inequality measurement and that on the discussion of the results of empirical analysis, has preferred to focus on income inequality. This paper looks into the analysis of wealth inequality, which can be performed by...