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Geodesic normal distribution on the circle. (English) Zbl 1410.60021

Summary: 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, \(2\pi \)) 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.

MSC:

60E05 Probability distributions: general theory
62E10 Characterization and structure theory of statistical distributions
62E15 Exact distribution theory in statistics
62F10 Point estimation

Software:

circular; CircStats
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References:

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