An extension of sine-skewed circular distributions

Abstract: Sine-skewed circular distributions are identifiable and have easily-computable trigonometric moments and a simple random number generation algorithm, whereas they are known to have relatively low levels of asymmetry. This study proposes a new family of circular distributions that can be skewed more significantly than that of existing models. It is shown that a subfamily of the proposed distributions is identifiable with respect to parameters and all distributions in the subfamily have explicit trigonometric moments and a simple random number generation algorithm. The maximum likelihood estimation for model parameters is considered and its finite sample performances are investigated by numerical simulations. Some real data applications are illustrated for practical purposes.