Majorization and the Lorenz Order with Applications in Applied Mathematics and Economics

  • Barry C. Arnold
  • José María Sarabia

Part of the Statistics for Social and Behavioral Sciences book series (SSBS)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Barry C. Arnold, José María Sarabia
    Pages 1-8
  3. Barry C. Arnold, José María Sarabia
    Pages 9-22
  4. Barry C. Arnold, José María Sarabia
    Pages 23-34
  5. Barry C. Arnold, José María Sarabia
    Pages 35-43
  6. Barry C. Arnold, José María Sarabia
    Pages 45-114
  7. Barry C. Arnold, José María Sarabia
    Pages 115-143
  8. Barry C. Arnold, José María Sarabia
    Pages 145-166
  9. Barry C. Arnold, José María Sarabia
    Pages 167-176
  10. Barry C. Arnold, José María Sarabia
    Pages 177-185
  11. Barry C. Arnold, José María Sarabia
    Pages 187-210
  12. Barry C. Arnold, José María Sarabia
    Pages 211-230
  13. Barry C. Arnold, José María Sarabia
    Pages 231-251
  14. Back Matter
    Pages 253-272

About this book


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


majorization Lorenz curve stochastic order multivariate distributions parametric forms income distributions Gini index forecasting ecological diversity inequality curve geometric inequality of Cesaro income

Authors and affiliations

  • Barry C. Arnold
    • 1
  • José María Sarabia
    • 2
  1. 1.Department of StatisticsUniversity of CaliforniaRiversideUSA
  2. 2.Department of EconomicsUniversity of CantabriaSantanderSpain

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing AG, part of Springer Nature 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-93772-4
  • Online ISBN 978-3-319-93773-1
  • Series Print ISSN 2199-7357
  • Series Online ISSN 2199-7365
  • Buy this book on publisher's site
Industry Sectors
Materials & Steel
Health & Hospitals
Finance, Business & Banking
IT & Software
Consumer Packaged Goods
Energy, Utilities & Environment
Oil, Gas & Geosciences