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2 results

  • Caracterisation des lois fortement unimodales

  • P. Capéraà
  • Journal:
    Advances in Applied Probability / Volume 18 / Issue 1 / March 1986
    Published online by Cambridge University Press:
    01 July 2016, pp. 277-278
    Print publication:
    March 1986
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  • Dispersive distributions, and the connection between dispersivity and strong unimodality

  • Toby Lewis, J. W. Thompson
  • Journal:
    Journal of Applied Probability / Volume 18 / Issue 1 / March 1981
    Published online by Cambridge University Press:
    14 July 2016, pp. 76-90
    Print publication:
    March 1981

  • Two continuous distributions, G, H so related that any two quantiles of H are more widely separated than the corresponding quantiles of G may be said to be ‘ordered in dispersion'; Saunders and Moran have given examples. It is shown here that distributions F (called ‘dispersive' distributions) exist, e.g. the exponential, such that if G, H are ordered in dispersion then so also are the convolutions F ∗G, F ∗H. The class of dispersive distributions is determined, and shown to coincide with the class of strongly unimodal distributions.