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  • Book
  • © 1987

Majorization and the Lorenz Order: A Brief Introduction

Authors:

  1. Barry C. Arnold

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

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

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Table of contents (7 chapters)

  1. Front Matter

    Pages N2-VI
    PDF

  2. Introduction

    • Barry C. Arnold
    Pages 1-9

  3. Majorization in IRn

    • Barry C. Arnold
    Pages 10-28

  5. Transformations and Their Effects

    • Barry C. Arnold
    Pages 45-56

  6. Multivariate and Stochastic Majorization

    • Barry C. Arnold
    Pages 57-76

  7. Some Related Orderings

    • Barry C. Arnold
    Pages 77-89

  8. Some Applications

    • Barry C. Arnold
    Pages 90-109

  9. Back Matter

    Pages 110-123
    PDF
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About this book

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.
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Authors and Affiliations

  • Department of Statistics, University of California, Riverside, USA

    Barry C. Arnold

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Bibliographic Information

  • Book Title: Majorization and the Lorenz Order: A Brief Introduction

  • Authors: Barry C. Arnold

  • Series Title: Lecture Notes in Statistics

  • DOI: https://doi.org/10.1007/978-1-4615-7379-1

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1987

  • Softcover ISBN: 978-0-387-96592-5Published: 05 November 1987

  • eBook ISBN: 978-1-4615-7379-1Published: 06 December 2012

  • Series ISSN: 0930-0325

  • Series E-ISSN: 2197-7186

  • Edition Number: 1

  • Number of Pages: VI, 122

  • Topics: Applications of Mathematics

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Buy it now

eBook USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

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