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

Pfyffer, Samuel ; Gatto, Riccardo

In: Computational Statistics, 2013, vol. 28, no. 1, p. 255-268

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    Title
    • An efficient simulation algorithm for the generalized von Mises distribution of order two
    Author
    • Pfyffer, Samuel. Physics Institute, Space Research and Planetary Sciences, University of Bern, Sidlerstrasse 5, 3012, Bern, Switzerland
    • Gatto, Riccardo. Institute of Mathematical Statistics and Actuarial Science, University of Bern, Alpeneggstrasse 22, 3012, Bern, Switzerland
    Document Type
    • Postprint
    OAI-PMH Identifier
    • oai:doc.rero.ch:312851
    Summary
    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 algorithm with 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