{"paper":{"title":"A note on the bivariate distribution representation of two perfectly correlated random variables by Dirac's $\\delta$-function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.NI","authors_text":"Andr\\'es Alay\\'on Glazunov, Jie Zhang","submitted_at":"2012-05-04T12:26:31Z","abstract_excerpt":"In this paper we discuss the representation of the joint probability density function of perfectly correlated continuous random variables, i.e., with correlation coefficients $\\rho=pm1$, by Dirac's $\\delta$-function. We also show how this representation allows to define Dirac's $\\delta$-function as the ratio between bivariate distributions and the marginal distribution in the limit $\\rho\\rightarrow \\pm1$, whenever this limit exists. We illustrate this with the example of the bivariate Rice distribution"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.0933","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"}