Discriminating Between the Von Mises and Wrapped Normal Distributions

Summary In the analysis of circular data, we encounter two models which lay claim to the title of normal distribution: the von Mises and wrapped normal distributions. In this paper, we consider whether it is possible to distinguish between them in a practical situation. More specifically, given data from a circular distribution which may be either von Mises or wrapped normal, we enquire as to how large a sample is required in order to tell them apart.