{"paper":{"title":"$L_p$-nested symmetric distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.OT","authors_text":"Fabian Sinz, Matthias Bethge","submitted_at":"2010-08-04T10:44:30Z","abstract_excerpt":"Tractable generalizations of the Gaussian distribution play an important role for the analysis of high-dimensional data. One very general super-class of Normal distributions is the class of $\\nu$-spherical distributions whose random variables can be represented as the product $\\x = r\\cdot \\u$ of a uniformly distribution random variable $\\u$ on the $1$-level set of a positively homogeneous function $\\nu$ and arbitrary positive radial random variable $r$. Prominent subclasses of $\\nu$-spherical distributions are spherically symmetric distributions ($\\nu(\\x)=\\|\\x\\|_2$) which have been further gen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.0740","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"}