In-depth Analysis of von Mises Distribution Models: Understanding Theory, Applications, and Future Directions

Multimodal and asymmetric circular data manifest in diverse disciplines, underscoring the significance of fitting suitable distributions for the analysis of such data. This study undertakes a comprehensive comparative assessment, encompassing diverse extensions of the von Mises distribution and the associated statistical methodologies, spanning from Richard von Mises' seminal work in 1918 to contemporary applications, with a particular focus on the field of wind energy. The primary objective is to discern the strengths and limitations inherent in each method. To illustrate the practical implications, three authentic datasets and a simulation study are incorporated to showcase the performance of the proposed models. Furthermore, this paper provides an exhaustive list of references pertinent to von Mises distribution models.