Related papers: On the Chebyshev's Inequality for Weighted Means

We give necessary and sufficient conditions for the Chebyshev inequality to be an equality.

We obtain some new inequalities of Chebyshev Type.

In this paper, we obtain a new generalization of Chebyshev's inequality for random elements taking values in a separate Banach space.

We show that a differential version of the classical Chebyshev-Markov-Stieltjes inequalities holds for a broad family of weight functions. Such a differential version appears to be new. Our results apply to weight functions which are…

In this article, we derive a new generalization of Chebyshev inequality for random vectors. We demonstrate that the new generalization is much less conservative than the classical generalization.

A variant of the well-known Chebyshev inequality for scalar random variables can be formulated in the case where the mean and variance are estimated from samples. In this paper we present a generalization of this result to multiple…

The idea of the restricted mean has been used to establish a significantly improved version of Markov's inequality that does not require any new assumptions. The result immediately extends on Chebyshev's inequalities and Chernoff's bound.…

In this paper, we derive new probability bounds for Chebyshev's inequality if the supremum of the probability density function is known. This result holds for one-dimensional or multivariate continuous probability distributions with finite…

We give here a simple proof of weighted logarithmic Sobolev inequality, for example for Cauchy type measures, with optimal weight, sharpening results of Bobkov-Ledoux. Some consequences are also discussed.

We provide a sufficient condition for a measure on the real line to satisfy a modified logarithmic Sobolev inequality, thus extending the criterion of Bobkov and G\"{o}tze. Under mild assumptions the condition is also necessary.…

In this work, a generalization of Chebyshev functional is presented. New inequalities of Gruss type via Pompeiu's mean value theorem are established. Improvements of some old inequalities are proved. A generalization of pre-Gruss inequality…

We provide a new characterization of the logarithmic Sobolev inequality.

This article describes a new proof of the equality condition for the Brunn-Minkowski inequality.

This paper aims to characterize the function appearing in the weighted Hermite-Hadamard inequality. We provide improved inequalities for the weighted means as applications of the obtained results. Modifications of the weighted…

In this note we prove a weighted version of the Khintchine inequalities.

The upper bound inequality for variance of weighted sum of correlated random variables is derived according to Cauchy-Schwarz's inequality, while the weights are non-negative with sum of 1. We also give a novel proof with positive…

We provide new sufficient conditions under which Ryser's conjecture holds.

In this paper, by using Jensen's inequality and Chebyshev integral inequality, some generalizations and new refined Hardy type integral inequalities are obtained. In addition, the corresponding reverse relation are also proved.

Certain excess versions of the Minkowski and H\"older inequalities are given. These new results generalize and improve the Minkowski and H\"older inequalities.

We give upper and lower bounds for weighted Chebyshev and residual polynomials on subsets of the real line. As an application, we prove a Szeg\H{o}-type theorem in the setting of Parreau--Widom sets.