Maximum likelihood estimation for the wrapped Cauchy distribution

The wrapped Cauchy distribution is an alternative to the Fisher-von Mises distribution for modeling symmetric data on the circle, and its maximum likelihood estimate (m.l.e.) represents a robust alternative to the mean direction for estimating the location for circular data. Surprisingly, there appear to be no previous results on the m.l.e. for the wrapped Cauchy distribution. It is shown that for sample sizes greater than two, the m.l.e. exists, is unique, and can be found by solving the likelihood equations. Also, a simple algorithm is presented which converges to the m.l.e.