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

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.

Keywords

Reference

Colombe Becquart, Aurore Archimbaud, Anne M. Ruiz, and Zaineb Smida, “A Note on the Folding Test of Unimodality: limitation and improved alternative”, arXiv, n. 2605.13326, May 2026.