# Bingham distribution

In statistics, the **Bingham distribution**, named after Christopher Bingham, is an antipodally symmetric probability distribution on the *n*-sphere.^{[1]} It is a generalization of the Watson distribution and a special case of the Kent and Fisher-Bingham distributions.

The Bingham distribution is widely used in paleomagnetic data analysis,^{[2]} and has been reported as being of use in the field of computer vision.^{[3]}^{[4]}^{[5]}

Its probability density function is given by

which may also be written

where **x** is an axis (i.e., a unit vector), *M* is an orthogonal orientation matrix, *Z* is a diagonal concentration matrix, and
is a confluent hypergeometric function of matrix argument.

## See also

## References

- ↑ Bingham, Ch. (1974) "An antipodally symmetric distribution on the sphere".
*Annals of Statistics*, 2(6):1201–1225. - ↑ Onstott, T.C. (1980) "Application of the Bingham distribution function in paleomagnetic studies".
*Journal of Geophysical Research*, 85:1500–1510. - ↑ S. Teller and M. Antone (2000).
*Automatic recovery of camera positions in Urban Scenes* - ↑ "Belief Propagation with Directional Statistics for Solving the Shape-from-Shading Problem". Springer. 2008. Retrieved November 29, 2013.
- ↑ "Better robot vision: A neglected statistical tool could help robots better understand the objects in the world around them.". MIT News. October 7, 2013. Retrieved October 7, 2013.

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