An Improved Laguerre-Samuelson Inequality of Chebyshev-Markov Type

Abstract EN

The Chebyshev-Markov extremal distributions by known moments to order four are used to improve the Laguerre-Samuelson inequality for finite real sequences.

In general, the refined bound depends not only on the sample size but also on the sample skewness and kurtosis.

Numerical illustrations suggest that the refined inequality can almost be attained for randomly distributed completely symmetric sequences from a Cauchy distribution.