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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.
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BibTeX
@misc{mcneil2026stochastic,
title = {{Stochastic Inversion of Multivariate Uniform-Distribution-Preserving Transformations}},
author = {Alexander J. McNeil and Johanna G. Nešlehová},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.07174},
eprint = {2607.07174},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.07174},
}
RIS
TY - UNPB
TI - Stochastic Inversion of Multivariate Uniform-Distribution-Preserving Transformations
AU - Alexander J. McNeil
AU - Johanna G. Nešlehová
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2607.07174
UR - https://arxiv.org/abs/2607.07174
AB - 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.
ER -