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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Year of publication:	2005
Authors:	Csiszar, Villo ; Móri, Tamás F. ; Székely, Gábor J.
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 71.2005, 4, p. 323-335
Publisher:	Elsevier
Subject:	Convexity Scale mixtures Bienayme-Chebyshev inequality

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10005137760