Becquart, Colombe, Archimbaud, Aurore, Ruiz-Gazen, Anne and Smida, Zaineb (2026) A Note on the Folding Test of Unimodality: limitation and improved alternative. arXiv, n. 2605.13326

Preview

Text Download (688kB) | Preview

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.