{"ID":6138163,"CreatedAt":"2026-07-09T01:07:32.349475501Z","UpdatedAt":"2026-07-11T09:01:53.812435343Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.07174","arxiv_id":"2607.07174","title":"Stochastic Inversion of Multivariate Uniform-Distribution-Preserving Transformations","abstract":"A multivariate transformation of the unit cube with component transformations that are piecewise continuously differentiable and uniform distribution preserving (udp) is considered. A stochastic inverse transformation is defined using randomization to overcome the non-injective nature of the udp transformations. The inverse transformation preserves the uniform margins of a random vector distributed according to a copula and yields different copulas for different randomizations. A copula density transformation result for the multivariate stochastic inverse is proved and illustrated in the bivariate case.","short_abstract":"A multivariate transformation of the unit cube with component transformations that are piecewise continuously differentiable and uniform distribution preserving (udp) is considered. A stochastic inverse transformation is defined using randomization to overcome the non-injective nature of the udp transformations. The in...","url_abs":"https://arxiv.org/abs/2607.07174","url_pdf":"https://arxiv.org/pdf/2607.07174v1","authors":"[\"Alexander J. McNeil\",\"Johanna G. Nešlehová\"]","published":"2026-07-08T09:09:06Z","proceeding":"math.ST","tasks":"[\"math.ST\"]","methods":"[]","has_code":false}