{"paper":{"title":"Weighted information and entropy rates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.PR"],"primary_cat":"cs.IT","authors_text":"Izabella Stuhl, Yuri Suhov","submitted_at":"2016-12-29T15:20:24Z","abstract_excerpt":"The weighted entropy $H^{\\rm w}_\\phi (X)=H^{\\rm w}_\\phi (f)$ of a random variable $X$ with values $x$ and a probability-mass/density function $f$ is defined as the mean value ${\\mathbb E} I^{\\rm w}_\\phi(X)$ of the weighted information $I^{\\rm w}_\\phi (x)=-\\phi (x)\\log\\,f(x)$. Here $x\\mapsto\\phi (x)\\in{\\mathbb R}$ is a given weight function (WF) indicating a 'value' of outcome $x$. For an $n$-component random vector ${\\mathbf{X}}_0^{n-1}=(X_0,\\ldots ,X_{n-1})$ produced by a random process ${\\mathbf{X}}=(X_i,i\\in{\\mathbb Z})$, the weighted information $I^{\\rm w}_{\\phi_n}({\\mathbf x}_0^{n-1})$ an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.09169","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"}