{"paper":{"title":"Erdelyi-Kober Fractional Integral Operators from a Statistical Perspective -I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"A.M. Mathai, H.J. Haubold","submitted_at":"2013-03-16T13:49:15Z","abstract_excerpt":"In this article we examine the densities of a product and a ratio of two real positive scalar random variables $x_1$ and $x_2$, which are statistically independently distributed, and we consider the density of the product $u_1=x_1x_2$ as well as the density of the ratio $u_2={{x_2}\\over{x_1}}$ and show that Kober operator of the second kind is available as the density of $u_1$ and Kober operator of the first kind is available as the density of $u_2$ when $x_1$ has a type-1 beta density and $x_2$ has an arbitrary density. We also give interpretations of Kober operators of the second and first k"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.3978","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"}