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Inequalities: Theory of Majorization and Its Applications

  • Book
  • © 2011

Overview

Authors:
  1. Albert W. Marshall

    1. Dept. Statistics, University of British Columbia, Vancouver, Canada

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    You can also search for this author in PubMed   Google Scholar

  2. Ingram Olkin

    1. Dept. Statistics, Stanford University, Stanford, USA

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    You can also search for this author in PubMed   Google Scholar

  3. Barry C. Arnold

    1. Dept. Statistics, University of California, Riverside, Riverside, USA

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Part of the book series: Springer Series in Statistics (SSS)

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Table of contents (21 chapters)

  1. Front Matter

    Pages i-xxviii
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  2. Theory of Majorization

    1. Front Matter

      Pages 1-1
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    2. Introduction

      • Albert W. Marshall, Ingram Olkin, Barry C. Arnold
      Pages 3-28

    3. Doubly Stochastic Matrices

      • Albert W. Marshall, Ingram Olkin, Barry C. Arnold
      Pages 29-77

    4. Schur-Convex Functions

      • Albert W. Marshall, Ingram Olkin, Barry C. Arnold
      Pages 79-154

    5. Equivalent Conditions for Majorization

      • Albert W. Marshall, Ingram Olkin, Barry C. Arnold
      Pages 155-163

    6. Preservation and Generation of Majorization

      • Albert W. Marshall, Ingram Olkin, Barry C. Arnold
      Pages 165-202

    7. Rearrangements and Majorization

      • Albert W. Marshall, Ingram Olkin, Barry C. Arnold
      Pages 203-239

  3. Mathematical Applications

    1. Front Matter

      Pages 241-241
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    2. Combinatorial Analysis

      • Albert W. Marshall, Ingram Olkin, Barry C. Arnold
      Pages 243-267

    3. Geometric Inequalities

      • Albert W. Marshall, Ingram Olkin, Barry C. Arnold
      Pages 269-296

    4. Matrix Theory

      • Albert W. Marshall, Ingram Olkin, Barry C. Arnold
      Pages 297-365

    5. Numerical Analysis

      • Albert W. Marshall, Ingram Olkin, Barry C. Arnold
      Pages 367-383

  4. Stochastic Applications

    1. Front Matter

      Pages 385-385
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    2. Stochastic Majorizations

      • Albert W. Marshall, Ingram Olkin, Barry C. Arnold
      Pages 387-440

    3. Probabilistic, Statistical, and Other Applications

      • Albert W. Marshall, Ingram Olkin, Barry C. Arnold
      Pages 441-526

    4. Additional Statistical Applications

      • Albert W. Marshall, Ingram Olkin, Barry C. Arnold
      Pages 527-574

  5. Generalizations

    1. Front Matter

      Pages 575-575
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    2. Orderings Extending Majorization

      • Albert W. Marshall, Ingram Olkin, Barry C. Arnold
      Pages 577-609

    3. Multivariate Majorization

      • Albert W. Marshall, Ingram Olkin, Barry C. Arnold
      Pages 611-633
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About this book

This book’s first edition has been widely cited by researchers in diverse fields. The following are excerpts from reviews. “Inequalities: Theory of Majorization and its Applications” merits strong praise. It is innovative, coherent, well written and, most importantly, a pleasure to read. … This work is a valuable resource!” (Mathematical Reviews). “The authors … present an extremely rich collection of inequalities in a remarkably coherent and unified approach. The book is a major work on inequalities, rich in content and original in organization.” (Siam Review). “The appearance of … Inequalities in 1979 had a great impact on the mathematical sciences. By showing how a single concept unified a staggering amount of material from widely diverse disciplines–probability, geometry, statistics, operations research, etc.–this work was a revelation to those of us who had been trying to make sense of his own corner of this material.” (Linear Algebra and its Applications). This greatly expanded new edition includes recent research on stochastic, multivariate and group majorization, Lorenz order, and applications in physics and chemistry, in economics and political science, in matrix inequalities, and in probability and statistics. The reference list has almost doubled.

Reviews

From the reviews of the second edition:

“The second edition of the praised classic without whom I know that some people never leave home … . attempts to bring these uses to the fore so that the reader can see the extent and variation in its use. The chapters of the original version remain intact … . The bibliography has increased by over 50%. … Needless to say, the revised volume obviously continues as a celebrated classic.” (Simo Puntanen, International Statistical Review, Vol. 79 (2), 2011)

Authors and Affiliations

  • Dept. Statistics, University of British Columbia, Vancouver, Canada

    Albert W. Marshall

  • Dept. Statistics, Stanford University, Stanford, USA

    Ingram Olkin

  • Dept. Statistics, University of California, Riverside, Riverside, USA

    Barry C. Arnold

About the authors

Albert W. Marshall is Professor Emeritus of Statistics at the University of British Columbia. His fundamental contributions to reliability theory have had a profound effect in furthering its development.

Ingram Olkin is Professor Emeritus of Statistics at Stanford University. He has made fundamental contributions in multivariate analysis, and in the development of statistical methods in meta-analysis, which have resulted in its use in many applications.

Barry C. Arnold is Distinguished Professor of Statistics at the University of California, Riverside. His previous books deal with Pareto Distributions, Order Statistics, Record Values, Conditionally Specified Distributions, and the Lorenz Order.

Bibliographic Information

  • Book Title: Inequalities: Theory of Majorization and Its Applications

  • Authors: Albert W. Marshall, Ingram Olkin, Barry C. Arnold

  • Series Title: Springer Series in Statistics

  • DOI: https://doi.org/10.1007/978-0-387-68276-1

  • Publisher: Springer New York, NY

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Science+Business Media, LLC 2011

  • Hardcover ISBN: 978-0-387-40087-7Published: 03 December 2010

  • Softcover ISBN: 978-1-4939-3827-8Published: 23 August 2016

  • eBook ISBN: 978-0-387-68276-1Published: 25 November 2010

  • Series ISSN: 0172-7397

  • Series E-ISSN: 2197-568X

  • Edition Number: 2

  • Number of Pages: XXVII, 909

  • Topics: Statistical Theory and Methods

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