On an extension of the von Mises distribution due to Batschelet

This paper considers the three-parameter family of symmetric unimodal circular distributions proposed by Batschelet in [1], an extension of the von Mises distribution containing distributional forms ranging from the highly leptokurtic to the very platykurtic. The family's fundamental properties are given, and likelihood-based techniques described which can be used to perform estimation and hypothesis testing. Analyses are presented of two data sets which illustrate how the family and three of its most direct competitors can be applied in the search for parsimonious models for circular data.