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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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    References listed on IDEAS

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    1. Mijatović, Aleksandar & Mramor, Veno & Uribe Bravo, Gerónimo, 2020. "A note on the exact simulation of spherical Brownian motion," Statistics & Probability Letters, Elsevier, vol. 165(C).
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    4. Eduardo Garcia-Portugues & Davy Paindaveine & Thomas Verdebout, 2020. "On optimal tests for rotational symmetry against new classes of hyperspherical distributions," Post-Print hal-03169388, HAL.
    5. Eduardo García-Portugués & Davy Paindaveine & Thomas Verdebout, 2020. "On Optimal Tests for Rotational Symmetry Against New Classes of Hyperspherical Distributions," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(532), pages 1873-1887, December.
    6. Saw, John G., 1984. "Ultraspherical polynomials and statistics on the m-sphere," Journal of Multivariate Analysis, Elsevier, vol. 14(1), pages 105-113, February.
    7. Gary Ulrich, 1984. "Computer Generation of Distributions on the M‐Sphere," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 33(2), pages 158-163, June.
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