Sharp inequalities of Bienaymé-Chebyshev and Gauß type for possibly asymmetric intervals around the mean

DOI10.1007/s11749-022-00844-9zbMath1523.60042arXiv2208.08813MaRDI QIDQ6051852

Roxana A. Ion, Edwin R. van den Heuvel, Chris A. J. Klaassen

Publication date: 20 September 2023

Published in: Test (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2208.08813

zbMATH Keywords

Jensen inequalityChebyshev's inequalityCantelli's inequalityKhintchine representation

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Applications of statistics in engineering and industry; control charts (62P30) Probability distributions: general theory (60E05) Nonparametric inference (62G99) Statistical distribution theory (62E99)

Cites Work

• ROC and the bounds on tail probabilities via theorems of Dubins and F. Riesz
• Squared skewness minus kurtosis bounded by 186/125 for unimodal distributions
• Generalized Gauss-Chebyshev inequalities for unimodal distributions
• Generalizations of some concentration inequalities
• Two-sided probability bound for a symmetric unimodal random variable
• The multiple Cantelli inequalities
• Shewhart’s Idea of Predictability and Modern Statistics
• Second-Order Exchangeability Analysis for Multimodel Ensembles
• On Tcebycheff's type inequalities
• Run Length Variability and Three Sigma Control Limits
• The multivariate Markov and multiple Chebyshev inequalities
• Best constants in Chebyshev inequalities with various applications.
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