The DOI matches its Crossref record.
An Antipodally Symmetric Distribution on the Sphere
Open accessAbstract
The distribution $\Psi(\mathbf{x}; Z, M) = \operatorname{const}. \exp(\mathrm{tr} (ZM^T \mathbf{xx}^T M))$ on the unit sphere in three-space is discussed. It is parametrized by the diagonal shape and concentration matrix $Z$ and the orthogonal orientation matrix $M. \Psi$ is applicable in the statistical analysis of measurements of random undirected axes. Exact and asymptotic sampling distributions are derived. Maximum likelihood estimators for $Z$ and $M$ are found and their asymptotic properties elucidated. Inference procedures, including tests for isotropy and circular symmetry, are proposed. The application of $\Psi$ is illustrated by a numerical example.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cited by
Jupp, P. E. (2005) · Encyclopedia of Statistical Sciences · doi:10.1002/0471667196.ess7086 · Cited by 282
Ball and rackets: inferring fiber fanning from diffusion-weighted MRI
Sotiropoulos, S. N., Behrens, T. E. J., & Jbabdi, S. (2012) · NeuroImage · doi:10.1016/j.neuroimage.2012.01.056 · Cited by 156
Bingham–NODDI: Mapping anisotropic orientation dispersion of neurites using diffusion MRI
Tariq, M., Schneider, T., Alexander, D. C., Gandini Wheeler-Kingshott, C. A., & Zhang, H. (2016) · NeuroImage · doi:10.1016/j.neuroimage.2016.01.046 · Cited by 169
Lampinen, B., Szczepankiewicz, F., Lätt, J., Knutsson, L., Mårtensson, J., Björkman-Burtscher, I. M., van Westen, D., Sundgren, P. C., Ståhlberg, F., & Nilsson, M. (2023) · NeuroImage · doi:10.1016/j.neuroimage.2023.120338 · Cited by 38
Simultaneous Localization and Mapping Using a Novel Dual Quaternion Particle Filter
Li, K., Kurz, G., Bernreiter, L., & Hanebeck, U. D. (2018) · 2018 21st International Conference on Information Fusion (FUSION) · doi:10.23919/icif.2018.8455347 · Cited by 13
Metadata
- Authors
- Bingham, C.
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 1974-11-01
- Volume
- 2
- Issue
- 6
- ISSN
- 0090-5364 (ISSN-L)
- OpenAlex
- W2070216603
- Cited by
- 570
- References
- 0
- FWCI
- 2.56
- Type
- journal article
- Language
- en
- Open access
- bronze
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: An Antipodally Symmetric Distribution on the Sphere. https://app.cochat.ai/papers/10.1214/aos/1176342874
- The paper
- Bingham, C. (1974). An Antipodally Symmetric Distribution on the Sphere. The Annals of Statistics. https://doi.org/10.1214/aos/1176342874
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
