{"paper":{"title":"An unbiased estimate for the mean of a {0,1} random variable with relative error distribution independent of the mean","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"Mark Huber","submitted_at":"2013-09-20T23:37:27Z","abstract_excerpt":"Say $X_1,X_2,\\ldots$ are independent identically distributed Bernoulli random variables with mean $p$. This paper builds a new estimate $\\hat p$ of $p$ that has the property that the relative error, $\\hat p /p - 1$, of the estimate does not depend in any way on the value of $p$. This allows the construction of exact confidence intervals for $p$ of any desired level without needing any sort of limit or approximation. In addition, $\\hat p$ is unbiased. For $\\epsilon$ and $\\delta$ in $(0,1)$, to obtain an estimate where $\\mathbb{P}(|\\hat p/p - 1| > \\epsilon) \\leq \\delta$, the new algorithm takes "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5413","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"}