Geodesic Normal distribution on the circle

Jean-François Coeurjolly 1, 2 Nicolas Le Bihan 2
1 FIGAL - Fiabilité et Géométrie Aléatoire
LJK - Laboratoire Jean Kuntzmann
2 GIPSA-CICS - CICS
GIPSA-DIS - Département Images et Signal
Abstract : 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.
Document type :
Journal articles
Metrika, Springer Verlag, 2012, 75 (7), pp.977-995. <10.1007/s00184-011-0363-7>


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Submitted on : Wednesday, February 23, 2011 - 8:04:25 AM
Last modification on : Saturday, February 13, 2016 - 9:01:26 PM
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Jean-François Coeurjolly, Nicolas Le Bihan. Geodesic Normal distribution on the circle. Metrika, Springer Verlag, 2012, 75 (7), pp.977-995. <10.1007/s00184-011-0363-7>. <hal-00548828v2>

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