Discrete mixture representations of spherical distributions

verfasst von

Ludwig Baringhaus, Rudolf Grübel

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.

Organisationseinheit(en)

Institut für Versicherungs- und Finanzmathematik

Typ

Artikel

Journal

Statistical papers

Band

65

Seiten

557-596

Anzahl der Seiten

40

ISSN

0932-5026

Publikationsdatum

04.2024

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Statistik und Wahrscheinlichkeit, Statistik, Wahrscheinlichkeit und Ungewissheit

Elektronische Version(en)

https://doi.org/10.48550/arXiv.2301.03870 (Zugang: Offen)
https://doi.org/10.1007/s00362-023-01393-5 (Zugang: Offen)