{"paper":{"title":"Practical Explicitly Invertible Approximation to 4 Decimals of Normal Cumulative Distribution Function Modifying Winitzki's Approximation of erf","license":"http://creativecommons.org/licenses/publicdomain/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Alessandro Soranzo, Emanuela Epure","submitted_at":"2012-11-27T19:53:21Z","abstract_excerpt":"We give a new explicitly invertible approximation of the normal cumulative distribution function: $\\Phi(x) \\simeq 1/2 + 1/2 \\sqrt{1-{e}^{-x^2\\frac{17+{x}^{2}}{26.694+2x^2}}}$, $\\forall x \\ge 0$, with absolute error $<4.00\\cdot 10^{-5}$, absolute value of the relative error $<4.53\\cdot 10^{-5}$, which, beeing designed essentially for practical use, is much simpler than a previously published formula and, though less precise, still reaches 4 decimals of precision, and has a complexity essentially comparable with that of the approximation of the normal cumulative distribution function $\\Phi(x)$ i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.6403","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"}