Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/309018 
Year of Publication: 
2023
Citation: 
[Journal:] Statistical Papers [ISSN:] 1613-9798 [Volume:] 65 [Issue:] 2 [Publisher:] Springer [Place:] Berlin, Heidelberg [Year:] 2023 [Pages:] 557-596
Publisher: 
Springer, Berlin, Heidelberg
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.
Subjects: 
Mixture distribution
Isotropy
Surface harmonics
Self-mixing stable distribution families
Almost sure representations
Skew product decomposition
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article
Document Version: 
Published Version

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