Y with a positive finite mean μY and the quantile function Q(x). The barycenter is denoted by μX and defined as the … area is μX − 1/2, and the Gini’s mean difference is 4μY (μX − 1/2). The same barycenter-based formulae hold for normalized …This paper introduces in statistics the notion of the barycenter of the distribution of a non-negative random variable …