Chebyshev-type inequalities for scale mixtures
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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Volume (Year): 71 (2005)
Issue (Month): 4 (March)
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- 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.
- 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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