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An Improved Laguerre-Samuelson Inequality of Chebyshev-Markov Type
An Improved Laguerre-Samuelson Inequality of Chebyshev-Markov Type
Werner Hürlimann
Swiss Mathematical Society, University of Fribourg, 1700 Fribourg, Switzerland
Received 2 May 2014; Accepted 29 July 2014; Published 12 August 2014
Academic Editor: Cheng-Hong Yang
Copyright © 2014 Werner Hürlimann. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
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.
1. Introduction
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