{"paper":{"title":"The median of a jittered Poisson distribution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Jean-Fran\\c{c}ois Coeurjolly, Jo\\\"elle Rousseau-Tr\\'epanier","submitted_at":"2019-01-16T16:15:03Z","abstract_excerpt":"Let $N_\\lambda$ and $U$ be two independent random variables respectively distributed as a Poisson distribution with parameter $\\lambda >0$ and a uniform distribution on $(0,1)$. This paper establishes that the median, say $M$, of $N_\\lambda+U$ is close to $\\lambda +1/3$ and more precisely that $M-\\lambda-1/3=o(\\lambda^{-1})$ as $\\lambda\\to \\infty$. This result is used to construt a very simple robust estimator of $\\lambda$ which is consistent and asymptotically normal. Compared to known robust estimates, this one can still be used with large datasets ($n\\simeq 10^9$)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.05367","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"}