, Volume 78, Issue 8, pp 997–1014 | Cite as

Schur properties of convolutions of gamma random variables

  • Farbod Roosta-KhorasaniEmail author
  • Gábor J. Székely


Sufficient conditions for comparing the convolutions of heterogeneous gamma random variables in terms of the usual stochastic order are established. Such comparisons are characterized by the Schur convexity properties of the cumulative distribution function of the convolutions. Some examples of the practical applications of our results are given.


Schur-convexity of tails Majorization order Linear combinations Gamma distribution Tail probabilities 

Mathematics Subject Classification

Primary 60E15 Secondary 62E99 



We wish to thank Profs. Milan Merkle and Maochao Xu for their great feedback during the preparation of the text. We would also like to thank the anonymous referee for many valuable comments which helped us improve the presentation and the content of this paper.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of British ColumbiaVancouverCanada
  2. 2.National Science FoundationArlingtonVirginia
  3. 3.Alfréd Rényi Institute of MathematicsHungarian Academy of SciencesBudapestHungary

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