aequationes mathematicae

, Volume 54, Issue 1–2, pp 173–180 | Cite as

Inequalities for sums of independent geometrical random variables

  • Milan Merkle
  • Ljiljana Petrović
Research Papers


We give a survey of known results regarding Schur-convexity of probability distribution functions. Then we prove that the functionF(p 1,...,pn;t)=P(X1+...+Xn≤t) is Schur-concave with respect to (p 1,...,pn) for every realt, whereX i are independent geometric random variables with parametersp i. A generalization to negative binomial random variables is also presented.

AMS subject classification (1991)

Primary 60E15 Secondary 62E99 


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Copyright information

© Birkhäuser Verlag 1997

Authors and Affiliations

  • Milan Merkle
    • 1
  • Ljiljana Petrović
    • 2
  1. 1.Faculty of Electrical EngineeringUniversity of BelgradeBelgradeYugoslavia
  2. 2.Faculty of ScienceUniversity of KragujevacKragujevacYugoslavia

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