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Statistics of Directional Data
Abstract
Summary: Directional data analysis is emerging as an important area of statistics. Within the past two decades, various new techniques have appeared, mostly to meet the needs of scientific workers dealing with directional data. The paper first introduces the two basic models for the multi-dimensional case known as the von Mises–Fisher distribution and the Bingham distribution. Their sampling distribution theory depends heavily on the isotropic case and some developments are discussed. An optimum property of an important test for the von Mises–Fisher case is established. A non-parametric test is proposed for the hypothesis of independence for observations on a torus. In addition to some numerical examples on the preceding topics, five case studies are given which illuminate the power of this new methodology. The case studies are concerned with cancer research, origins of comets, arrival times of patients, navigational problems and biological rhythms. Some unsolved problems are also indicated.
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Cited by
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Alignment of fibroblasts on grooved surfaces described by a simple geometric transformation
Dunn, G. A., & Brown, A. F. (1986) · Journal of Cell Science · doi:10.1242/jcs.83.1.313 · Cited by 335
Jupp, P. E. (2005) · Encyclopedia of Statistical Sciences · doi:10.1002/0471667196.ess7086 · Cited by 282
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Banca, P., Herrojo Ruiz, M., Gonzalez-Zalba, M. F., Biria, M., Marzuki, A. A., Piercy, T., Sule, A., Fineberg, N. A., & Robbins, T. W. (2024) · eLife · doi:10.7554/elife.87346 · Cited by 9
Metadata
- Authors
- Mardia, K. V.
- Venue
- Journal of the Royal Statistical Society Series B: Statistical Methodology
- Publisher
- Oxford University Press (OUP)
- Published
- 1975-07-01
- Volume
- 37
- Issue
- 3
- Pages
- 349-371
- ISSN
- 1369-7412 (ISSN-L)
- 1467-9868
- OpenAlex
- W4289256549
- Cited by
- 525
- References
- 0
- FWCI
- 5.89
- Type
- journal article
- Language
- en
- Open access
- closed
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- Mardia, K. V. (1975). Statistics of Directional Data. Journal of the Royal Statistical Society Series B: Statistical Methodology. https://doi.org/10.1111/j.2517-6161.1975.tb01550.x
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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.
