A wrapped flexible generalized skew-normal model for a bimodal circular distribution of wind directions

Motivated by the analysis of wind directions, in this paper we consider skew-symmetric circular distributions generated by perturbation of a symmetric circular distribution. This class of models is able to describe different distribution shapes, including symmetric, skewed, and bimodal, which are often observed in circular data, as in our motivating example of wind directions at a site in Spain. We propose a wrapped version of the flexible generalized skew-normal distribution to fit these data. The model is presented and the parameters of the proposed model are estimated by the maximum likelihood method. We also note that in the considered area, typical sea breeze and land breeze directions are observed. Thus, we consider a subdivision of the data to fit these directions separately. The likelihood ratio test shows that the proposed model outperforms the wrapped skew-normal, and the Akaike information criterion reveals that it fits our wind-direction data with comparable performances with respect to other well-known bimodal circular distributions.