  This paper is concerned with the study of a circular random distribution
called geodesic Normal distribution recently proposed for general manifolds.
This distribution, parameterized by two real numbers associated to some
specific location and dispersion concepts, looks like a standard Gaussian on
the real line except that the support of this variable is $[0,2\pi)$ and that
the Euclidean distance is replaced by the geodesic distance on the circle. Some
properties are studied and comparisons with the von Mises distribution in terms
of intrinsic and extrinsic means and variances are provided. Finally, the
problem of estimating the parameters through the maximum likelihood method is
investigated and illustrated with some simulations.
