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.