Given that the Lorenz curve is widely used for analyzing income distribution and inequality, this study introduces an alternative functional form for the Lorenz curve that is constructed based on the weighted average of the exponential function and the functional form implied by Pareto...

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...

Similar looking Lorenz Curves can imply very different income density functions and potentially lead to wrong policy implications regarding inequality. This paper derives a relation between a Lorenz Curve and the modality of its underlying income density: Given a parametric Lorenz Curve, it is...

This paper is concerned with the problem of ranking Lorenz curves in situations where the Lorenz curves intersect and no unambiguous ranking can be attained without introducing weaker ranking criteria than first-degree Lorenz dominance. To deal with such situations two alternative sequences of...

This paper is concerned with the problem of ranking Lorenz curves in situations where the Lorenz curves intersect and no unambiguous ranking can be attained without introducing weaker ranking criteria than first-degree Lorenz dominance. To deal with such situations Aaberge (2009) introduced two...

This paper surveys selected applications of the Lorenz curve and related stochastic orders in economics and econometrics, with a bias towards problems in statistical distribution theory. These include characterizations of income distributions in terms of families of inequality measures, Lorenz...

Index of refraction is found to be a good measure of economic inequality within the Lorenz curve framework. It has origin in geometrical optics, where it measures bending of a ray of light passing from one transparent medium into another. As light refracts according to characteristics of...

An ideal state of development, when viewed with fantasy, is nothing but a state or condition where light touches everybody without refraction. The diagonal line of the Lorenz Curve Framework represents such an ideal condition. In the presence of inequality, however, it deviates or refracts from...

This article provides a tool to study over time the distributions of income in a population, regardless the irregular distribution of data. We even approach Lorenz curves at the times when we lack the required data. Finally we apply the present technique to a European country where inequalities...