• Albert W. Marshall
  • Ingram Olkin
  • Barry C. Arnold
Part of the Springer Series in Statistics book series (SSS)


There is a certain intuitive appeal to the vague notion that the 2 components of a vectorxare “less spread out” or “more nearly equal” 3 than are the components of a vectory. Not surprisingly, the notion 4 arises in a variety of contexts, and it can be made precise in a number 5 of ways. But in remarkably many cases, the appropriate precise state- 6 ment is that “xis majorized byy” (writtenx <yand defined ahead 7 in Definition A.1). Some of these cases are reviewed here.


Convex Function Convex Hull Partial Order Income Inequality Lorenz Curve 
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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Albert W. Marshall
    • 1
    • 2
  • Ingram Olkin
    • 3
  • Barry C. Arnold
    • 4
  1. 1.Department of StatisticsUniversity of British ColumbiaVancouverCanada
  2. 2.Lummi IslandUSA
  3. 3.Department of StatisticsStanford UniversityStanfordUSA
  4. 4.Department of StatisticsUniversity of CaliforniaRiversideUSA

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