Estimation of finite mixture models of skew-symmetric circular distributions

Analysis of circular data is challenging, since the usual statistical methods are unsuitable and it is necessary to use circular periodic probabilistic models. Because some actual circular datasets exhibit asymmetry and/or multimodality, finite mixtures of symmetric circular distributions to model and fit these data have been investigated. However, it is necessary to question the predominant assumption that each component in the finite mixture model is symmetric. In this study, we consider a finite mixture model of possibly skewed circular distributions and discuss the expectation-maximization (EM) algorithm for the maximum likelihood estimate. It is shown that the maximum likelihood estimator is strongly consistent under some suitable conditions in a finite mixture of skew-symmetric circular distributions. A modified M-step in the EM algorithm is proposed in order to estimate the unknown parameter vectors effectively. To investigate the performance of our proposed model with its estimation procedure, we provide a numerical example as well as data analysis using the records of the time of day of fatal traffic accidents.