{"paper":{"title":"An improvement of the Berry--Esseen inequality with applications to Poisson and mixed Poisson random sums","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Irina Shevtsova, Victor Korolev","submitted_at":"2009-12-15T20:46:08Z","abstract_excerpt":"By a modification of the method that was applied in (Korolev and Shevtsova, 2009), here the inequalities $$\\rho(F_n,\\Phi)\\le\\frac{0.335789(\\beta^3+0.425)}{\\sqrt{n}}$$ and $$\\rho(F_n,\\Phi)\\le \\frac{0.3051(\\beta^3+1)}{\\sqrt{n}} $$ are proved for the uniform distance $\\rho(F_n,\\Phi)$ between the standard normal distribution function $\\Phi$ and the distribution function $F_n$ of the normalized sum of an arbitrary number $n\\ge1$ of independent identically distributed random variables with zero mean, unit variance and finite third absolute moment $\\beta^3$. The first of these inequalities sharpens t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.2795","kind":"arxiv","version":2},"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"}