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.
Type de document :
Article dans une revue
Metrika, Springer Verlag, 2012, 75 (7), pp.977-995. <10.1007/s00184-011-0363-7>


https://hal.archives-ouvertes.fr/hal-00548828
Contributeur : Jean-François Coeurjolly <>
Soumis le : mercredi 23 février 2011 - 08:04:25
Dernière modification le : samedi 13 février 2016 - 21:01:26
Document(s) archivé(s) le : mardi 24 mai 2011 - 03:11:13

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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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