On Convergence in the Mean for Densities

DOI10.1137/1107039zbMath0302.60015OpenAlexW2009249423MaRDI QIDQ4057356

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Publication date: 1963

Published in: Theory of Probability & Its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/1107039

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Probability distributions: general theory (60E05)

Related Items (13)

Convergence in total variation to a mixture of Gaussian laws ⋮ Rate of convergence and Edgeworth-type expansion in the entropic central limit theorem ⋮ Convergence in distribution norms in the CLT for non identical distributed random variables ⋮ Berry-Esseen bounds in the entropic central limit theorem ⋮ Asymptotically optimal Berry-Esseen-type bounds for distributions with an absolutely continuous part ⋮ Convergence in Law Implies Convergence in Total Variation for Polynomials in Independent Gaussian, Gamma or Beta Random Variables ⋮ The entropic Erdős-Kac limit theorem ⋮ Non-uniform bounds in local limit theorems in case of fractional moments. I ⋮ Rényi divergence and the central limit theorem ⋮ Non-uniform bounds in local limit theorems in case of fractional moments. II ⋮ Penultimate gamma approximation in the CLT for skewed distributions ⋮ Asymptotic development for the CLT in total variation distance ⋮ A note on approximations in random variate generation

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