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Some characterizations of unimodal distribution functions

  • E. M. J. Bertin
  • W. Hengartner
  • R. Theodorescu
Article

Abstract

Let F be a distribution function and let QF(l)=0 for l<0 and QF(l)= sup {F(x+l)−F(x): x∈ℝ} for l≧0 be its Lévy concentration function. This paper has two purposes: to give a characterization of unimodal distribution functions (Theorem 3.5) and a representation theorem for the class of unimodal distribution functions (Theorem 6.2), both in terms of their Lévy concentration functions.

Keywords

Distribution Function Stochastic Process Probability Theory Mathematical Biology Representation Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • E. M. J. Bertin
    • 1
  • W. Hengartner
    • 2
  • R. Theodorescu
    • 2
  1. 1.Department of MathematicsUniversity of UtrechtUtrechtNetherlands
  2. 2.Dept. of MathematicsLaval UniversityCanada

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