Circular Outliers Detection Using a Mixture of Von Mises Distributions

Circular data are typical examples of directional data with a specific regular period‎. ‎Because the presence of outliers leads to invalid statistical inferences on the parameters of the circular regression models‎, ‎their prevalence in analyzing these models requires particular attentions‎. ‎There are different approaches for modeling the structure of the data set with outliers in which using the mixture models is among the most important ones‎. ‎As a new idea‎, ‎to study the methods in determining the outlier data and to employ the mixture model of Von Mises distribution are considered in this paper‎. ‎The EM algorithm is utilized to estimate the parameters of these models‎. ‎The performance of the proposed models is investigated using some simulation studies, and then the confusion matrix is considered to evaluate the accuracy of fitting models. ‎Also‎, ‎the proposed methods are applied to analyze a real data set‎, ‎related to the wave directional analysis in the Bushehr province in Iran.