Chebyshev-type inequalities for scale mixtures

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

Statistics & Probability Letters, 2005, vol. 71, issue 4, 323-335

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 .

Keywords: Convexity; Scale; mixtures; Bienayme-Chebyshev; inequality (search for similar items in EconPapers)
Date: 2005
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