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Characterizations of unimodal distribution functions

  • E. M. J. Bertin
  • R. Theodorescu
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 861)

Abstract

This paper has two purposes: to give a characterization of unimodal distribution functions (Theorem 2.2) and a representation theorem for the class of unimodal distribution functions (Theorem 3.3), both in terms of their Lévy concentration functions.

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References

  1. [1]
    Bertin, E.M.J., Hengartner, W., and Theodorescu, R., Some characterizations of unimodal distribution functions. Preprint 116, University of Utrecht, Department of Mathematics, 1979.Google Scholar
  2. [2]
    Bertin, E.M.J., and Theodorescu, R., Some characterizations of discrete unimodality. Preprint 173, University of Utrecht, Department of Mathematics, 1980.Google Scholar
  3. [3]
    Hengartner, W., and Theodorescu, R., Concentration functions. Academic Press, New York 1973; revised Russian version, Nauka, Moscow 1980.zbMATHGoogle Scholar
  4. [4]
    Hengartner, W., and Theodorescu, R., A characterization of strictly unimodal distribution functions by their concentration functions. Publ. Inst. Statist. Paris 24 (1978), 1–10.MathSciNetzbMATHGoogle Scholar
  5. [5]
    Lukacs, E., Characteristic functions. 2nd ed., Hafner Publ. Co., New York 1970.zbMATHGoogle Scholar
  6. [6]
    Medgyessi, P., Decomposition of superpositions of density functions and discrete distributions. Adam Hilger, Bristol 1977.Google Scholar

Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • E. M. J. Bertin
    • 1
  • R. Theodorescu
    • 2
  1. 1.Mathematisch InstituutRijksuniversiteit UtrechtUtrecht
  2. 2.Dépt. de Math.Université LavalQuébec

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