2014/04/30 by Lutz Mattner, Mattner, Lutz, Jona Schulz +1 · 1 citation
Mathematics · #60F05 (Primary) 60E15 (Secondary) #Advanced Statistical Methods and Models #FOS: Mathematics #Mathematical Inequalities and Applications #Mathematical functions and polynomials #Probability (math.PR) #math.PR #msc:60E15 #msc:60F05
paper · pdf · doi:10.48550/arxiv.1404.7657
arxiv created 2014/04/30 · openalex publication_date 2014/04/30 · arxiv updated 2014/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Kolmogorov distances between a symmetric hypergeometric law with standard deviation σ and its usual normal approximations are computed and shown to be less than 1/(√(8π) σ), with the order 1/σ and the constant 1/√(8π) being optimal. The results of Hipp and Mattner (2007) for symmetric binomial laws are obtained as special cases. Connections to Berry-Esseen type results in more general situations concerning sums of simple random samples or Bernoulli convolutions are explained. Auxiliary results of independent interest include rather sharp normal distribution function inequalities, a simple identifiability result for hypergeometric laws, and some remarks related to Lévy's concentration-variance inequality.