相关论文: Center-Outward Multiple-Output Lorenz Curves and G…
All multivariate extensions of the univariate theory of risk measurement run into the same fundamental problem of the absence, in dimension d > 1, of a canonical ordering of Rd. Based on measure transportation ideas, several attempts have…
Univariate concepts as quantile and distribution functions involving ranks and signs, do not canonically extend to $\mathbb{R}^d, d\geq 2$. Palliating that has generated an abundant literature. Chapter 1 shows that, unlike the many…
Quantiles are a fundamental concept in probability and theoretical statistics and a daily tool in their applications. While the univariate concept of quantiles is quite clear and well understood, its multivariate extension is more…
We propose center-outward superquantile and expected shortfall functions, with applications to multivariate risk measurements, extending the standard notion of value at risk and conditional value at risk from the real line to…
The classical Lorenz curve is often used to depict inequality in a population of incomes, and the associated Gini coefficient is relied upon to make comparisons between different countries and other groups. The sample estimates of these…
Modeling equity in the allocation of scarce resources is a fast-growing concern in the humanitarian logistics field. The Gini coefficient is one of the most widely recognized measures of inequity and it was originally characterized by means…
This article focuses on some properties of three tools used to measure economic inequalities with respect to a distribution of wealth $\mu$: Gini coefficient $G$, Hoover coefficient or Robin Hood coefficient $H$, and the Lorenz…
Social inequality manifested across different strata of human existence can be quantified in several ways. Here we compute non-entropic measures of inequality such as Lorenz curve, Gini index and the recently introduced $k$ index…
The Gini's mean difference was defined as the expected absolute difference between a random variable and its independent copy. The corresponding normalized version, namely Gini's index, denotes two times the area between the egalitarian…
We propose an extension of the univariate Lorenz curve and of the Gini coefficient to the multivariate case, i.e., to simultaneously measure inequality in more than one variable. Our extensions are based on copulas and measure inequality…
Given that the existing parametric functional forms for the Lorenz curve do not fit all possible size distributions, a universal parametric functional form is introduced. By using the empirical data from different scientific disciplines and…
To generalize the notion of distribution function to dimension $d\geq 2$, in the recent papers it was proposed a concept of center-outward distribution function based on optimal transportation ideas, and the inferential properties of the…
Extending rank-based inference to a multivariate setting such as multiple-output regression or MANOVA with unspecified d-dimensional error density has remained an open problem for more than half a century. None of the many solutions…
Based on the novel concept of multivariate center-outward quantiles introduced recently in Chernozhukov et al. (2017) and Hallin et al. (2021), we are considering the problem of nonparametric multiple-output quantile regression. Our…
We consider concepts and models for measuring inequality in the distribution of resources with a focus on how inequality varies as a function of covariates. Lorenz introduced a device for measuring inequality in the distribution of income…
We examine whether mobility measures appropriately represent changes in individual status, like income or ranks. We suggest three elementary principles for mobility comparisons and show that many commonly used indices violate one or more of…
Lorenz values and the Gini index are popular quantities in Mathematical Economics, and are used here in the context of quantum systems with finite-dimensional Hilbert space. They quantify the uncertainty in the probability distribution…
Entropy is being used in physics, mathematics, informatics and in related areas to describe equilibration, dissipation, maximal probability states and optimal compression of information. The Gini index on the other hand is an established…
For a probability P in $R^d$ its center outward distribution function $F_{\pm}$, introduced in Chernozhukov et al. (2017) and Hallin et al. (2021), is a new and successful concept of multivariate distribution function based on mass…
We find the set of extremal points of Lorenz curves with fixed Gini index and compute the maximal $L^1$-distance between Lorenz curves with given values of their Gini coefficients. As an application we introduce a bidimensional index that…