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Discrete mixture representations of spherical distributions

Author

Listed:
  • Ludwig Baringhaus

    (Leibniz Universität Hannover)

  • Rudolf Grübel

    (Leibniz Universität Hannover)

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.

Suggested Citation

  • Ludwig Baringhaus & Rudolf Grübel, 2024. "Discrete mixture representations of spherical distributions," Statistical Papers, Springer, vol. 65(2), pages 557-596, April.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:2:d:10.1007_s00362-023-01393-5
    DOI: 10.1007/s00362-023-01393-5
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