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Geodesic normal distribution on the circle


  • Jean-François Coeurjolly


  • Nicolas Bihan


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, 2π) 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. Copyright Springer-Verlag 2012

Suggested Citation

  • Jean-François Coeurjolly & Nicolas Bihan, 2012. "Geodesic normal distribution on the circle," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(7), pages 977-995, October.
  • Handle: RePEc:spr:metrik:v:75:y:2012:i:7:p:977-995
    DOI: 10.1007/s00184-011-0363-7

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    1. Simons, Robert, 1990. "The role of management control systems in creating competitive advantage: New perspectives," Accounting, Organizations and Society, Elsevier, vol. 15(1-2), pages 127-143.
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