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.
@article{arxiv.2605.13326,
title = {A Note on the Folding Test of Unimodality: limitation and improved alternative},
author = {Colombe Becquart and Aurore Archimbaud and Anne M. Ruiz and Zaineb Smida},
journal= {arXiv preprint arXiv:2605.13326},
year = {2026}
}