UC Santa Barbara

We show that the operations of mixing and wrapping linear distributionsaround a unit circle commute, and can produce a wide variety of circularmodels. In particular, we show that many wrapped circular models studied inthe literature can be obtained as scale mixtures of just the wrapped Gaussianand the wrapped exponential distributions, and inherit many properties fromthese two basic models. We also point out how this general approach canproduce flexible asymmetric circular models, the need for which has beennoted by many authors.