Stochastic Ordering

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


The notion of stochastic ordering for random variables is a familiar and useful concept. A basic reference is Lehmann (1955). More recent work, with many results in stochastic ordering and further references, is in Stoyan (1977, 1983). However, the most comprehensive discussion of stochastic and related orders is given by Shaked and Shanthikumar (2007), to which frequent reference is made in this chapter. Other useful references are Szekli (1995) and Müller and Stoyan (2002).


Convex Cone Gini Index Stochastic Dominance Lorenz Curve Quantile Function 
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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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