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Logarithmic Concavity of Distribution Functions

  • Milan Merkle
Chapter
Part of the Mathematics and Its Applications book series (MAIA, volume 430)

Abstract

We give sufficient conditions for a probability distribution function to be logarithmically concave. The limiting behaviour of corresponding inequalities is discussed.

Key words and phrases

Convexity Schur-convexity Logarithmic convexity and concavity Distribution functions 

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References

  1. 1.
    E. Artin, The Gamma Function, Holt, Rinehart and Winston, New York, 1964 [Translation from the German original from 1931].zbMATHGoogle Scholar
  2. 2.
    A. Fransen and S. Wrigge Calculation of the moments and the moment generating function for the reciprocal gamma distribution, Math. Comp. 42 (1984), 601–616.MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    A. Marshall and I. Olkin, Inequalities: Theory of Majorization and Its Applications, Academic Press, New York, 1979.zbMATHGoogle Scholar
  4. 4.
    M. Merkle and Lj. Petrovic, On Schur-convexity of some distribution functions, Publ. Inst. Math. 56 (70) (1994), 111–118.MathSciNetGoogle Scholar
  5. 5.
    D. S. Mitrinović, Analytic Inequalities, Springer Verlag, Berlin — Heidelberg — New York, 1970.zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Milan Merkle
    • 1
  1. 1.Faculty of Electrical EngineeringUniversity of BelgradeBelgradeYugoslavia

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