The Lorenz curve for assessing economic inequality depicts the relation between two cumulative distribution functions (CDFs), one for the distribution of incomes or wealth and the other for their first-moment distribution. By contrast, the receiver operating characteristic (ROC) curve for evaluating diagnostic systems depicts the relation between the complements of two CDFs, one for the distrib...

The Lorenz curve for assessing economic inequality depicts the relation between two cumulative distribution functions (CDFs), one for the distribution of incomes or wealth and the other for their first-moment distribution. By contrast, the receiver operating characteristic (ROC) curve for evaluating diagnostic systems depicts the relation between the complements of two CDFs, one for the distrib...

Background and Aim: Equitable distribution of health sector resources has always been one of the major challenges of this sector. Due to health care needs, equitable distribution of physicians is a determining factor in health system policies. The purpose of this study was to investigate the distribution of justice among the general practitioners and specialists in Khuzestan province. Materia...

The Lorenz curve of a Zipf function describes, graphically, the relation between the fraction of the items and the fraction of the sources producing these items. Hence it generalizes the socalled 80/20-rule to general fractions. In this paper we examine the relation of such Lorenz curves with the size of the system (expressed by the total number of sources). We prove that the height of such a L...

Several indices based on the receiver operating characteristic curve (ROC curve) have previously been found to possess probabilistic interpretations. However, these interpretations are based on some unrealistic diagnostic scenarios. In this paper, the author presents a new approach using the Lorenz curve. The author found that the summary indices of the Lorenz curve, that is, the Pietra index a...

In this paper hybrid Lorenz curves are proposed as a way of circumventing an important drawback of traditional models of the Lorenz curve, namely lack of satisfactory fit over the entire range of a given income distribution. Two categories of hybrid models are identified, namely the additive models and the multiplicative models. Whereas the additive models are obtained by taking convex combinat...

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 ordering of multiparameter distributions in terms of their parameters, probability inequalities for di...