Discrete mixture representations of spherical distributions

authored by

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.

Organisation(s)

Institute of Actuarial and Financial Mathematics

Type

Article

Journal

Statistical papers

Volume

65

Pages

557-596

No. of pages

40

ISSN

0932-5026

Publication date

04.2024

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Statistics and Probability, Statistics, Probability and Uncertainty

Electronic version(s)

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