Displaying similar documents to “On the Bennett–Hoeffding inequality”

A note on optimal probability lower bounds for centered random variables

Mark Veraar (2008)

Colloquium Mathematicae

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We obtain lower bounds for ℙ(ξ ≥ 0) and ℙ(ξ > 0) under assumptions on the moments of a centered random variable ξ. The estimates obtained are shown to be optimal and improve results from the literature. They are then applied to obtain probability lower bounds for second order Rademacher chaos.

Gaussian Approximation of Moments of Sums of Independent Random Variables

Marcin Lis (2012)

Bulletin of the Polish Academy of Sciences. Mathematics

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We continue the research of Latała on improving estimates of the pth moments of sums of independent random variables with logarithmically concave tails. We generalize some of his results in the case of 2 ≤ p ≤ 4 and present a combinatorial approach for even moments.

Strong Convergence for weighed sums of negatively superadditive dependent random variables

Zhiyong Chen, Haibin Wang, Xuejun Wang, Shuhe Hu (2016)

Kybernetika

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In this paper, the strong law of large numbers for weighted sums of negatively superadditive dependent (NSD, in short) random variables is obtained, which generalizes and improves the corresponding one of Bai and Cheng ([2]) for independent and identically distributed random variables to the case of NSD random variables.

On asymptotic behaviors and convergence rates related to weak limiting distributions of geometric random sums

Tran Loc Hung, Phan Tri Kien, Nguyen Tan Nhut (2019)

Kybernetika

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Geometric random sums arise in various applied problems like physics, biology, economics, risk processes, stochastic finance, queuing theory, reliability models, regenerative models, etc. Their asymptotic behaviors with convergence rates become a big subject of interest. The main purpose of this paper is to study the asymptotic behaviors of normalized geometric random sums of independent and identically distributed random variables via Gnedenko's Transfer Theorem. Moreover, using the...