{"paper":{"title":"A Kolmogorov-Smirnov type test for two inter-dependent random variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","physics.data-an","stat.AP","stat.TH"],"primary_cat":"math.PR","authors_text":"Tommy Liu","submitted_at":"2018-02-27T14:28:32Z","abstract_excerpt":"Consider $n$ iid random variables, where $\\xi_1, \\ldots, \\xi_n$ are $n$ realisations of a random variable $\\xi$ and $\\zeta_1, \\ldots, \\zeta_n$ are $n$ realisations of a random variable $\\zeta$. The distribution of each realisation of $\\xi$, that is the distribution of \\emph{one} $\\xi_i$, depends on the value of the corresponding $\\zeta_i$, that is the probability $P\\left(\\xi_i\\leq x\\right)=F(x,\\zeta_i)$. We develop a statistical test to see if the $\\xi_1, \\ldots, \\xi_n$ are distributed according to the distribution function $F(x,\\zeta_i)$. We call this new statistical test the condition Kolmog"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.09899","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"}