Modelling asymmetrically distributed circular data using the wrapped skew-normal distribution

We consider problems of inference for the wrapped skew-normal distribution on the circle. A centered parametrization of the distribution is introduced, and simulation used to compare the performance of method of moments and maximum likelihood estimation for its parameters. Maximum likelihood estimation is shown, in general, to be superior. The operating characteristics of two moment based tests, for wrapped normal and wrapped half-normal parent populations, respectively, are also explored. The former test is easy to apply, maintains the nominal significance level well and is generally highly powerful. The latter test does not hold the nominal significance level so well, although it is very powerful against negatively skew alternatives. Likelihood based tests for the two distributions are also discussed. A real data set from the ornithological literature is used to illustrate the application of the developed methodology and its extension to finite mixture modelling. Received: September 2003/ Revised: April 2005