Jean-Jacques Rousseau wrote in the Preface to his famous Discourse on Inequality that “I consider the subject of the following discourse as one of the most interesting questions philosophy can propose, and unhappily for us, one of the most thorny that philosophers can have to solve. For how shall we know the source of inequality between men, if we do not begin by knowing mankind?” (Rousseau, 1754). This citation of Rousseau appears in an article in Spanish where Dagum (2001), in the memory of whom this book is published, also cites Socrates who said that the only useful knowledge is that which makes us better and Seneca who wrote that knowing what a straight line is, is not important if we do not know what rectitude is. These references are indeed a good illustration of Dagum’s vast knowledge, which was clearly not limited to the ?eld of Economics. For Camilo the ?rst part of Rousseau’s citation certainly justi?ed his interest in the ?eld of inequality which was at the centre of his scienti?c preoccupations. It should however be stressed that for Camilo the second part of the citation represented a “solid argument in favor of giving macroeconomic foundations to microeconomic behavior” (Dagum, 2001). More precisely, “individualism and methodological holism complete each other in contributing to the explanation of individual and social behavior” (Dagum, 2001).

Deals with income distribution methods and their economic applications.

This book was written to serve as a graduate-level textbook for special topics classes in mathematics, statistics, and economics, to introduce these topics to other researchers, and for use in short courses. It is an introduction to the theory of majorization and related notions, and contains detailed material on economic applications of majorization and the Lorenz order, investigating the theoretical aspects of these two interrelated orderings. Revising and expanding on an earlier monograph, Majorization and the Lorenz Order: A Brief Introduction, the authors provide a straightforward development and explanation of majorization concepts, addressing historical development of the topics, and providing up-to-date coverage of families of Lorenz curves. The exposition of multivariate Lorenz orderings sets it apart from existing treatments of these topics. Mathematicians, theoretical statisticians, economists, and other social scientists who already recognize the utility of the Lorenz order in income inequality contexts and arenas will find the book useful for its sound development of relevant concepts rigorously linked to both the majorization literature and the even more extensive body of research on economic applications. Barry C. Arnold, PhD, is Distinguished Professor in the Statistics Department at the University of California, Riverside. He is a Fellow of the American Statistical Society, the American Association for the Advancement of Science, and the Institute of Mathematical Statistics, and is an elected member of the International Statistical Institute. He is the author of more than two hundred publications and eight books. José María Sarabia, PhD, is Professor of Statistics and Quantitative Methods in Business and Economics in the Department of Economics at the University of Cantabria, Spain. He is author of more than one hundred and fifty publications and ten books and is an associate editor of several journals including TEST, Communications in Statistics, and Journal of Statistical Distributions and Applications.

The first monograph in econophysics focussed on the analyses and modelling of these distributions, ideal for physicists and economists.

This volume is mainly concerned with methods of estimating income elasticity. It is connected with economic development that can be achieved by reducing income inequality, a highly relevant subject in today’s world for a wide range of policy areas.

This text examines the underlying principles of inequality measurement and its relation to welfare economics, distributional analysis, and information theory. The book covers modern theoretical developments in inequality analysis, as well as showing how the way we think about inequality today has been shaped by classic contributions in economics and related disciplines.

Have gaps in health outcomes between the poor and better off grown? Are they larger in one country than another? Are health sector subsidies more equally distributed in some countries than others? Are health care payments more progressive in one health care financing system than another? What are catastrophic payments and how can they be measured? How far do health care payments impoverish households? Answering questions such as these requires quantitative analysis. This in turn depends on a clear understanding of how to measure key variables in the analysis, such as health outcomes, health expenditures, need, and living standards. It also requires set quantitative methods for measuring inequality and inequity, progressivity, catastrophic expenditures, poverty impact, and so on. This book provides an overview of the key issues that arise in the measurement of health variables and living standards, outlines and explains essential tools and methods for distributional analysis, and, using worked examples, shows how these tools and methods can be applied in the health sector. The book seeks to provide the reader with both a solid grasp of the principles underpinning distributional analysis, while at the same time offering hands-on guidance on how to move from principles to practice.