Finding exclusive peak with permutation testing

Comparing distributions is a crucial part of statistical work and supports decision-making across diverse fields. Various statistical tools address the task, evaluating central tendency, shape, and dispersion. This paper introduces a novel permutation-based methodology to compare distributions from a different perspective. In real-world scenarios, the objective may be to identify a product or service that clearly outperforms all competitors, if such an entity exists. To achieve this, we have implemented a method to compare exclusive peaks. Our approach relies on NonParametric Combination methodology and offers flexibility without distributional assumptions, making it particularly suitable to multivariate problems. In this paper we outline the methodology, conduct simulation studies, and conclude with insights for practical applications.