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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 13, Fasc. 2,
pages 293 - 310
 

EXTENSIONS OF CHEBYCHEV’S INEQUALITY WITH APPLICATIONS

Peter J. Bickel
Abba M. Krieger

Abstract: Chebychev’s inequality provides a bound on P[|X - m|> ks], where X has an arbitrary cdf F with s2 < oo . We extend this result by placing further restrictions on F. We first assume that X is n times divisible so that X can be viewed as an average of n i.i.d. random variables.

Camp-Meidell’s inequality provides a tighter bound than Chebychev’s by assuming that X is absolutely continuous with unimodal density function. We also extend this inequality by placing additional smoothness assumptions on the density of X.

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -

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