{"paper":{"title":"Center of mass and the optimal quantizers for some continuous and discrete uniform distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Mrinal Kanti Roychowdhury","submitted_at":"2017-07-06T04:08:13Z","abstract_excerpt":"In this paper, we first consider a flat plate (called a lamina) with uniform density $\\rho$ that occupies a region $\\mathfrak R$ of the plane. We show that the location of the center of mass, also known as the centroid, of the region equals the expected vector of a bivariate continuous random variable with a uniform probability distribution taking values on the region $\\mathfrak R$. Using this property, we prove that the Voronoi regions of an optimal set of two-means with respect to the uniform distribution defined on a disc partition the disc into two regions bounded by the semicircles. Besid"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.01630","kind":"arxiv","version":3},"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"}