Discrete mixture representations of spherical distributions

Ludwig Baringhaus () and Rudolf Grübel ()
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Ludwig Baringhaus: Leibniz Universität Hannover
Rudolf Grübel: Leibniz Universität Hannover

Statistical Papers, 2024, vol. 65, issue 2, No 3, 557-596

Abstract: Abstract We obtain discrete mixture representations for parametric families of probability distributions on Euclidean spheres, such as the von Mises–Fisher, the Watson and the angular Gaussian families. In addition to several special results we present a general approach to isotropic distribution families that is based on density expansions in terms of special surface harmonics. We discuss the connections to stochastic processes on spheres, in particular random walks, discrete mixture representations derived from spherical diffusions, and the use of Markov representations for the mixing base to obtain representations for families of spherical distributions.

Keywords: Mixture distribution; Isotropy; Surface harmonics; Self-mixing stable distribution families; Almost sure representations; Skew product decomposition; Primary 62H11; secondary 60E05 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00362-023-01393-5

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