An efficient simulation algorithm for the generalized von Mises distribution of order two

In this article we propose an exact efficient simulation algorithm for the
generalized von Mises circular distribution of order two. It is an acceptance-rejection
algorithmwith a piecewise linear envelope based on the local extrema and the inflexion
points of the generalized von Mises density of order two. We show that these points
can be obtained from the roots of polynomials and degrees four and eight, which can
be easily obtained by the methods of Ferrari and Weierstrass. A comparative study
with the von Neumann acceptance-rejection, with the ratio-of-uniforms and with a
Markov chain Monte Carlo algorithms shows that this new method is generally the
most efficient.