Abstract
Let F be a distribution function and let Q F(l)=0 for l<0 and Q F(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.
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Work supported by the Natural Sciences and Engineering Research Council Canada Grants A-7339 and A-7223, by the Québec Action Concertée Grant ER-1023, and by the Deutsche Forschungsgemeinschaft
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Bertin, E.M.J., Hengartner, W. & Theodorescu, R. Some characterizations of unimodal distribution functions. Z. Wahrscheinlichkeitstheorie verw Gebiete 57, 327–338 (1981). https://doi.org/10.1007/BF00534827
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DOI: https://doi.org/10.1007/BF00534827