On the circle, as on the line, families of unimodal distributions with parameters controlling location, scale or concentration, skewness and, in some appropriate sense, kurtosis, are useful for robust modelling. Although numerous such families now exist on the line, fewer exist on the circle.
In this talk we present a family of four-parameter distributions for circular data by taking a new approach. Properties of the proposed family include: unimodality; a simple characteristic function and tractable density and distribution functions; interpretable parameters individually measuring location, concentration, skewness and kurtosis, respectively; a wide range of skewness and "kurtosis"; some submodels including the wrapped Cauchy and cardioid distributions; closure under convolution and multiplication by certain constants; straightforward parameter estimation by both method of moments (suitable for smaller samples and moderate parameter values) and maximum likelihood. We will show that our new proposal compares favourably with some of the current four-parameter unimodal families on the circle. An illustrative application of the proposed model is given.