Details
| Original language | English |
|---|---|
| Pages (from-to) | 557-596 |
| Number of pages | 40 |
| Journal | Statistical papers |
| Volume | 65 |
| Issue number | 2 |
| Early online date | 15 Feb 2023 |
| Publication status | Published - 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
- Mathematics(all)
- Statistics and Probability
- Decision Sciences(all)
- Statistics, Probability and Uncertainty
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In: Statistical papers, Vol. 65, No. 2, 04.2024, p. 557-596.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Discrete mixture representations of spherical distributions
AU - Baringhaus, Ludwig
AU - Grübel, Rudolf
N1 - Funding Information: Open Access funding enabled and organized by Projekt DEAL.
PY - 2024/4
Y1 - 2024/4
N2 - 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.
AB - 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.
KW - Almost sure representations
KW - Isotropy
KW - Mixture distribution
KW - Primary 62H11
KW - secondary 60E05
KW - Self-mixing stable distribution families
KW - Skew product decomposition
KW - Surface harmonics
UR - http://www.scopus.com/inward/record.url?scp=85148086136&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2301.03870
DO - 10.48550/arXiv.2301.03870
M3 - Article
AN - SCOPUS:85148086136
VL - 65
SP - 557
EP - 596
JO - Statistical papers
JF - Statistical papers
SN - 0932-5026
IS - 2
ER -