{"paper":{"title":"On the Generalized Hill Process for Small Parameters and Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Aliou Diop, El Hadji Deme, Gane Samb Lo","submitted_at":"2011-11-19T15:06:25Z","abstract_excerpt":"Let $X_{1},X_{2},...$ be a sequence of independent copies (s.i.c) of a real random variable (r.v.) $X\\geq 1$, with distribution function $df$ $F(x)=\\mathbb{P}% (X\\leq x)$ and let $X_{1,n}\\leq X_{2,n} \\leq ... \\leq X_{n,n}$ be the order statistics based on the $n\\geq 1$ first of these observations. The following continuous generalized Hill process {equation*} T_{n}(\\tau)=k^{-\\tau}\\sum_{j=1}^{j=k}j^{\\tau}(\\log X_{n-j+1,n}-\\log X_{n-j,n}), \\label{dl02} {equation*} $\\tau >0$, $1\\leq k \\leq n$, has been introduced as a continuous family of estimators of the extreme value index, and largely studied "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.4564","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"}