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Chebyshev-type inequalities for scale mixtures

Author

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  • Csiszar, Villo
  • Móri, Tamás F.
  • Székely, Gábor J.

Abstract

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 .

Suggested Citation

  • Csiszar, Villo & Móri, Tamás F. & Székely, Gábor J., 2005. "Chebyshev-type inequalities for scale mixtures," Statistics & Probability Letters, Elsevier, vol. 71(4), pages 323-335, March.
    • Handle: RePEc:eee:stapro:v:71:y:2005:i:4:p:323-335
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    References listed on IDEAS

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    1. Thomas Sellke, 1996. "Generalized gauss-chebyshev inequalities for unimodal distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 43(1), pages 107-121, December.
    2. N. H. Bingham & Rudiger Kiesel, 2002. "Semi-parametric modelling in finance: theoretical foundations," Quantitative Finance, Taylor & Francis Journals, vol. 2(4), pages 241-250.
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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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