We propose a nonparametric estimator of the Lorenz curve that satisfies its theoretical properties, including monotonicity and convexity. We adopt a transformation approach that transforms a constrained estimation problem into an unconstrained one, which is estimated nonparametrically. We utilize the splines to facilitate the numerical implementation of our estimator and to provide a parametric...

The classical Lorenz curve visualizes and measures the disparity of items which are characterized by a single variable: The more the curve bends, the more scatter the data. Recently a general approach has been proposed and investigated that measures the disparity of multidimensioned items regardless of their dimension. This paper surveys various generalizations of Lorenz curve and Lorenz domina...

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 the sign of its third derivative which indicates whether the density is unimodal or zeromodal (i.e. do...

The purpose of this paper is to justify the use of the Gini coefficient and two close relatives for summarizing the basic information of inequality in distributions of income. To this end we employ a specific transformation of the Lorenz curve, the scaled conditional mean curve, rather than the Lorenz curve as the basic formal representation of inequality in distributions of income. The scaled ...

The most common data source on income distribution in China is grouped data. When income data is in grouped form, some acceptable Lorenz model is needed to approximate the underlying Lorenz curve. This paper presents a new family of Lorenz curves and shows that the main model of our proposed family of Lorenz curves outperforms other popular Lorenz curve models using data on US income distributi...

Background: One of the important aspects of equity in health is equality in the distribution of resources in this sector. The present study aimed to assess the distribution of hospital beds in Shiraz in 2014.   Methods: In this retrospective cross-sectional study, the population density index and fair distribution of beds were analyzed by Lorenz curve and Gini coefficient, respectively....

Lorenz curve and Gini index are the famous tools of income inequality. When one wants to study income inequality of a class of individuals, Partial Lorenz Curve is introduced and the corresponding measure of inequality called Partial Gini Index is defined. Partial Gini Index (PGI) is derived on Partial Lorenz Curve (PLC). Partial orderings are defined for comparison of partial Lorenz curves. Fo...