Symmetric circular models through duplication and cosine perturbation

Models for circular data displaying two diametrically opposed modes are considered. A general construction which can be used to generate such models, founded upon doubling the argument of a base symmetric unimodal distribution and cosine perturbation, is proposed. Fundamental properties of the resulting models are described, as are those of a particularly flexible family of distributions and three of its submodels. Parameter estimation via the method of moments and maximum likelihood is discussed, and a likelihood-ratio test for antipodal symmetry developed. The application of the proposed models and inferential methods is illustrated using two animal orientation data sets.

► Models for circular data displaying two diametrically opposed modes are considered. ► A general model-generating construction is proposed. ► Fundamental properties of the generated models are described. ► Inference based on the method of moments and maximum likelihood is discussed. ► Analyses of two animal orientation data sets illustrate the models and methodology.