Discrete mixture representations of spherical distributions

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Authors

  • Ludwig Baringhaus
  • Rudolf Grübel
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Details

Original languageEnglish
Pages (from-to)557-596
Number of pages40
JournalStatistical papers
Volume65
Issue number2
Early online date15 Feb 2023
Publication statusPublished - Apr 2024

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

    Almost sure representations, Isotropy, Mixture distribution, Primary 62H11, secondary 60E05, Self-mixing stable distribution families, Skew product decomposition, Surface harmonics

ASJC Scopus subject areas

Cite this

Discrete mixture representations of spherical distributions. / Baringhaus, Ludwig; Grübel, Rudolf.
In: Statistical papers, Vol. 65, No. 2, 04.2024, p. 557-596.

Research output: Contribution to journalArticleResearchpeer review

Baringhaus L, Grübel R. Discrete mixture representations of spherical distributions. Statistical papers. 2024 Apr;65(2):557-596. Epub 2023 Feb 15. doi: 10.48550/arXiv.2301.03870, 10.1007/s00362-023-01393-5
Baringhaus, Ludwig ; Grübel, Rudolf. / Discrete mixture representations of spherical distributions. In: Statistical papers. 2024 ; Vol. 65, No. 2. pp. 557-596.
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