EXTENSIONS OF CHEBYCHEV’S INEQUALITY WITH APPLICATIONS

Peter J. Bickel Abba M. Krieger

Abstract: Chebychev’s inequality provides a bound on where has an
arbitrary cdf with We extend this result by placing further restrictions on
We first assume that is times divisible so that can be viewed as an average of
i.i.d. random variables.

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