In recent years, there has been a significant increase in interest in lexical semantic change
detection. Many are the existing approaches, data used, and evaluation strategies to detect
semantic shifts. The classification of change words against stable words requires thresholds to
label the degree of semantic change. In this work, we compare state-of-the-art computational
historical linguistics approaches to evaluate the efficacy of thresholds based on the Gaussian
Distribution of semantic shifts. We present the results of an in-depth analysis conducted on
both SemEval-2020 Task 1 Subtask 1 and DIACR-Ita tasks. Specifically, we compare Temporal
Random Indexing, Temporal Referencing, Orthogonal Procrustes Alignment, Dynamic Word
Embeddings and Temporal Word Embedding with a Compass. While results obtained with
Gaussian thresholds achieve state-of-the-art performance in English, German, Swedish and
Italian, they remain far from results obtained using the optimal threshold
