Related papers: A New Generalization of Chebyshev Inequality for R…

We derive simple concentration inequalities for bounded random vectors, which generalize Hoeffding's inequalities for bounded scalar random variables. As applications, we apply the general results to multinomial and Dirichlet distributions…

In this paper, we present a novel generalization of the classical Ceva theorem to arbitrarily dimensional simplexes. Our approach allows cevians to have any dimension (smaller than the dimension of the base simplex). Consequently, our…

In this short note, we give a very simple but useful generalization of a result of Vershynin (Theorem 5.39 of [1]) for a random matrix with independent sub-Gaussian rows. We also explain with an example where our generalization is useful.

Some new bounds for the Chebychev functional of a pair of vectors in inner product spaces are pointed out. Reverses for the celebrated Jensen's inequality for convex functions defined on inner product spaces are given as well.

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

We establish a new extremal property of the classical Chebyshev polynomials in the context of best rank-one approximation of tensors. We also give some necessary conditions for a tensor to be a minimizer of the ratio of spectral and…

We establish estimates for the Lebesgue parameters of the Chebyshev Weak Thresholding Greedy Algorithm in the case of general bases in Banach spaces. These generalize and slightly improve earlier results in [9], and are complemented with…

We utilize operational methods to generalize the Chernoff inequality and prove a new result that relates the moment bound to strictly absolute monotonic functions. We show that the Chernoff bound is part of a continuum of probability…

In this paper we give a generalization of a result of Wei.

We give a very simple proof of a strengthened version of Chernoff's Inequality. We derive the same conclusion from much weaker assumptions.

This study is an example of a solid connection between fractional analysis and inequality theory, and includes new inequalities of the P\'{o}lya-Szeg% \"{o}-Chebyshev type obtained with the help of Generalized Proportional Fractional…

It is shown that at least 50% of the probability mass of a sum of independent Rademacher random variables is within one standard deviation from its mean. This lower bound is sharp, it is much better than for instance the bound that can be…

Generalized Chebyshev acceleration is a semi-iterative technique applicable to a basic iterative method only when the eigenvalues of the iteration matrix satisfy a highly restrictive inclusion condition. In this work, we relax this…

The object of this paper is to generalize a theorem on the binomial coefficient [4] to the case in an arithmetic progression. We will also give a slightly stronger result than Langevin's [2].

Proceeding the study of local properties of analytic functions started in [Br] we prove new dimensionless inequalities for such functions in terms of their Chebyshev degree. As a consequence, we obtain the reverse Holder inequalities for…

We propose a new approach for deriving probabilistic inequalities based on bounding likelihood ratios. We demonstrate that this approach is more general and powerful than the classical method frequently used for deriving concentration…

We modify the classical Bernstein's inequality for the sums of independent centered random variables (r.v.) in the terms of relative tails or moments. We built also some examples in order to show the exactness of offered results.

Chebyshev's inequality provides an upper bound on the tail probability of a random variable based on its mean and variance. While tight, the inequality has been criticized for only being attained by pathological distributions that abuse the…

The Chebyshev expansion offers a numerically efficient and easy-implement algorithm for evaluating dynamic correlation functions using matrix product states (MPS). In this approach, each recursively generated Chebyshev vector is…

A generalization of Mercer inequality for h-convex function is presented. As application, a weighted generalization of triangle inequality is given.