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.

翻译：本文指出了单峰性折叠检验（Folding Test of Unimodality, FTU）的一个关键局限性。在某些单变量混合分布设定下，基于折叠的准则可能系统性失效，将明显多峰的分布错误判定为单峰。我们完整刻画了狄拉克混合分布中此类失效的特征，并将分析推广至高斯混合分布。随后，我们引入一种捕获互补信息的双折叠程序，据此提出一种新检验方法——双折叠单峰性检验（Double Folding Test of Unimodality）。该方法解决了FTU的失效问题，并在模拟实验中提升了多峰性检测能力。