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Chebyshev-type inequalities for scale mixtures


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  • Csiszar, Villo
  • Móri, Tamás F.
  • Székely, Gábor J.
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    For important classes of symmetrically distributed random variables X the smallest constants C[alpha] are computed on the right-hand side of Chebyshev's inequality P(X[greater-or-equal, slanted]t)[less-than-or-equals, slant]C[alpha]EX[alpha]/t[alpha]. For example if the distribution of X is a scale mixture of centered normal random variables, then the smallest C2=0.331... and, as [alpha]-->[infinity], the smallest C[alpha][downwards arrow]0 and .

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 71 (2005)
    Issue (Month): 4 (March)
    Pages: 323-335

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    Handle: RePEc:eee:stapro:v:71:y:2005:i:4:p:323-335

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    Keywords: Convexity Scale mixtures Bienayme-Chebyshev inequality;


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    1. N. H. Bingham & Rudiger Kiesel, 2002. "Semi-parametric modelling in finance: theoretical foundations," Quantitative Finance, Taylor & Francis Journals, vol. 2(4), pages 241-250.
    2. Thomas Sellke, 1996. "Generalized gauss-chebyshev inequalities for unimodal distributions," Metrika, Springer, vol. 43(1), pages 107-121, December.
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    Cited by:
    1. Adell, José A. & Lekuona, Alberto, 2006. "Every random variable satisfies a certain nontrivial integrability condition," Statistics & Probability Letters, Elsevier, vol. 76(15), pages 1603-1606, September.


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