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© 2011

Inequalities: Theory of Majorization and Its Applications

Book

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

Table of contents

  1. Front Matter
    Pages i-xxviii
  2. Theory of Majorization

    1. Front Matter
      Pages 1-1
    2. Albert W. Marshall, Ingram Olkin, Barry C. Arnold
      Pages 3-28
    3. Albert W. Marshall, Ingram Olkin, Barry C. Arnold
      Pages 29-77
    4. Albert W. Marshall, Ingram Olkin, Barry C. Arnold
      Pages 79-154
    5. Albert W. Marshall, Ingram Olkin, Barry C. Arnold
      Pages 155-163
    6. Albert W. Marshall, Ingram Olkin, Barry C. Arnold
      Pages 165-202
    7. Albert W. Marshall, Ingram Olkin, Barry C. Arnold
      Pages 203-239
  3. Mathematical Applications

    1. Front Matter
      Pages 241-241
    2. Albert W. Marshall, Ingram Olkin, Barry C. Arnold
      Pages 243-267
    3. Albert W. Marshall, Ingram Olkin, Barry C. Arnold
      Pages 269-296
    4. Albert W. Marshall, Ingram Olkin, Barry C. Arnold
      Pages 297-365
    5. Albert W. Marshall, Ingram Olkin, Barry C. Arnold
      Pages 367-383
  4. Stochastic Applications

    1. Front Matter
      Pages 385-385
    2. Albert W. Marshall, Ingram Olkin, Barry C. Arnold
      Pages 387-440
    3. Albert W. Marshall, Ingram Olkin, Barry C. Arnold
      Pages 441-526
    4. Albert W. Marshall, Ingram Olkin, Barry C. Arnold
      Pages 527-574
  5. Generalizations

    1. Front Matter
      Pages 575-575
    2. Albert W. Marshall, Ingram Olkin, Barry C. Arnold
      Pages 577-609
    3. Albert W. Marshall, Ingram Olkin, Barry C. Arnold
      Pages 611-633

About this book

Introduction

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.

Authors and affiliations

  1. 1.Dept. StatisticsUniversity of British ColumbiaVancouverCanada
  2. 2.Dept. StatisticsStanford UniversityStanfordUSA
  3. 3.Dept. StatisticsUniversity of California, RiversideRiversideUSA

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
  • Series Abbreviated Title Springer Ser.Statistics
  • DOI https://doi.org/10.1007/978-0-387-68276-1
  • Copyright Information Springer Science+Business Media, LLC 2011
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-0-387-40087-7
  • Softcover ISBN 978-1-4939-3827-8
  • eBook ISBN 978-0-387-68276-1
  • Series ISSN 0172-7397
  • Series E-ISSN 2197-568X
  • Edition Number 2
  • Number of Pages XXVII, 909
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Statistical Theory and Methods
  • Buy this book on publisher's site
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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)