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arXiv · 2605.13326

A Note on the Folding Test of Unimodality: limitation and improved alternative

Colombe Becquart·Aurore Archimbaud·Anne M. Ruiz·Zaineb Smida
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Abstract

This note addresses a key limitation of the Folding Test of Unimodality (FTU). In specific univariate mixture settings, the folding-based criterion can systematically fail, misclassifying clearly multimodal distributions as unimodal. We fully characterize these failures for Dirac mixtures and extend the analysis to Gaussian mixtures. We then introduce a double-folding procedure that captures complementary information, leading to a new test, the Double Folding Test of Unimodality. It resolves the FTU failures and improves multimodality detection power in simulations.

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Colombe Becquart, Aurore Archimbaud, Anne M. Ruiz, Zaineb Smida. 2026-05-13. A Note on the Folding Test of Unimodality: limitation and improved alternative. https://arxiv.org/abs/2605.13326

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