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arXiv · 2607.07174

Stochastic Inversion of Multivariate Uniform-Distribution-Preserving Transformations

Alexander J. McNeil·Johanna G. Nešlehová
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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.

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Alexander J. McNeil, Johanna G. Nešlehová. 2026-07-08. Stochastic Inversion of Multivariate Uniform-Distribution-Preserving Transformations. https://arxiv.org/abs/2607.07174

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