Outlier detection in circular simultaneous functional relationship model (CSFRM) for unequal variances

This paper introduces the SFDMCEc statistic, a novel method for outlier detection in the Circular Simultaneous Functional Relationship Model (CSFRM) for unequal variances. Based on the circular distance cosine, the statistic effectively quantifies deviations in circular data. Its important properties are thoroughly investigated through simulation studies to establish critical cutoff points and evaluate detection power. The results demonstrate that the SFDMCEc statistic is highly effective in identifying outliers, particularly exhibiting superior performance for smaller sample sizes and larger concentration parameters at fixed contamination levels. The practical example of the proposed method is validated using real wind and wave direction data from Humberside, United Kingdom. The application confirms that the SFDMCEc statistic successfully identifies outliers, proving its effectiveness within the CSFRM framework when unequal variances are present. These findings suggest that the SFDMCEc statistic provides a valuable and reliable tool for researchers analyzing circular data in applied environmental and engineering contexts.