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Lorenz Surfaces Based on the Sarmanov-Lee Distribution with Applications to Multidimensional Inequality in Well-Being

Abstract: The purpose of this paper is to derive analytic expressions for the multivariate Lorenz surface for a relevant type of models based on the class of distributions with given marginals described by Sarmanov and Lee. The expression of the bivariate Lorenz surface can be conveniently interpreted as the convex linear combination of products of classical and concentrated univariate Lorenz curves. Thus, the generalized Gini index associated with this surface is expressed as a function of marginal Gini indices and concentration indices. This measure is additively decomposable in two factors, corresponding to inequality within and between variables. We present different parametric models using several marginal distributions including the classical Beta, the GB1, the Gamma, the lognormal distributions and others. We illustrate the use of these models to measure multidimensional inequality using data on two dimensions of well-being, wealth and health, in five developing countries

 Fuente: Mathematics 2020, 8(11), 2095

Editorial: MDPI

 Año de publicación: 2020

Nº de páginas: 17

Tipo de publicación: Artículo de Revista

 DOI: 10.3390/math8112095

ISSN: 2227-7390

Proyecto español: PID2019-105986GB-C22

Url de la publicación: https://doi.org/10.3390/math8112095