Exact bounds on the closeness between the Student and standard normal distributions

DOI10.1051/ps/2014014zbMath1332.62054arXiv1101.3328OpenAlexW2963677282MaRDI QIDQ2786466

Iosif Pinelis

Publication date: 12 February 2016

Published in: ESAIM: Probability and Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1101.3328

zbMATH Keywords

Kolmogorov distanceprobability inequalitiestotal variation distanceStudent's distributionstandard normal distribution

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Inequalities; stochastic orderings (60E15) Exact distribution theory in statistics (62E15) Approximations to statistical distributions (nonasymptotic) (62E17)

Related Items (8)

Distances between distributions via Stein's method ⋮ On the \(T\)-test ⋮ Dimension-agnostic inference using cross U-statistics ⋮ Nonparametric predictive distributions based on conformal prediction ⋮ Complete asymptotic expansions for the density function of \(t\)-distribution ⋮ Bounding distributional errors via density ratios ⋮ Complete asymptotic expansions related to the probability density function of the χ2-distribution ⋮ Monotone tail and moment ratio properties of Student's family of distributions

Cites Work

• Error bounds for asymptotic expansion of the scale mixtures of the normal distribution
• Variational inequalities with examples and an application to the central limit theorem
• Malliavin Calculus and Self Normalized Sums
• Tail Areas of the t-Distribution from a Mills'-Ratio-Like Expansion
• A Useful Convergence Theorem for Probability Distributions

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