{"paper":{"title":"On the absolute constants in the Berry-Esseen type inequalities for identically distributed summands","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Irina Shevtsova","submitted_at":"2011-11-28T19:18:37Z","abstract_excerpt":"By a modification of the method that was applied in (Korolev and Shevtsova, 2010), here the inequalities $\\Delta_n\\leq0.3328(\\beta_3+0.429)/\\sqrt{n}$ and $\\Delta_n\\leq0.33554(\\beta_3+0.415)/\\sqrt{n}$ are proved for the uniform distance $\\Delta_n$ between the standard normal distribution function and the distribution function of the normalized sum of an arbitrary number $n\\geq1$ of independent identically distributed random variables with zero mean, unit variance and finite third absolute moment $\\beta_3$. The first of these two inequalities improves one that was proved in (Korolev and Shevtsov"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.6554","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}