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.
