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Majorization and the Lorenz Order: A Brief Introduction

  • Barry C. Arnold

Part of the Lecture Notes in Statistics book series (LNS, volume 43)

Table of contents

  1. Front Matter
    Pages N2-VI
  2. Barry C. Arnold
    Pages 1-9
  3. Barry C. Arnold
    Pages 10-28
  4. Barry C. Arnold
    Pages 45-56
  5. Barry C. Arnold
    Pages 57-76
  6. Barry C. Arnold
    Pages 77-89
  7. Barry C. Arnold
    Pages 90-109
  8. Back Matter
    Pages 110-123

About this book

Introduction

My interest in majorization was first spurred by Ingram aIkin's proclivity for finding Schur convex functions lurking in the problem section of every issue of the American Mathematical Monthly. Later my interest in income inequality led me again to try and "really" understand Hardy, Littlewood and Polya' s contributions to the majori­ zation literature. I have found the income distribution context to be quite convenient for discussion of inequality orderings. The pre­ sent set of notes is designed for a one quarter course introducing majorization and the Lorenz order. The inequality principles of Dalton, especially the transfer or Robin Hood principle, are given appropriate prominence. Initial versions of these notes were used in graduate statistics classes taught at the Colegio de Postgraduados, Chapingo, Mexico and the University of California, Riverside. I am grateful to students in these classes for their constructive critical commentaries. My wife Carole made noble efforts to harness my free form writ­ ing and punctuation. Occasionally I was unmoved by her requests for clarification. Time will probably prove her right in these instances also. Peggy Franklin did an outstanding job of typing the manu­ script, and patiently endured requests for innumerable modifications.

Keywords

DEX Star design distribution equality form function functions inequality interaction matrices median reliability selection transformation

Authors and affiliations

  • Barry C. Arnold
    • 1
  1. 1.Department of StatisticsUniversity of CaliforniaRiversideUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4615-7379-1
  • Copyright Information Springer-Verlag New York 1987
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-96592-5
  • Online ISBN 978-1-4615-7379-1
  • Series Print ISSN 0930-0325
  • Buy this book on publisher's site