In statistics, the Bingham distribution, named after Christopher Bingham, is an antipodally symmetric probability distribution on the n-sphere.Bingham, Ch. (1974) "An antipodally symmetric distribution on the sphere". Annals of Statistics, 2(6):1201–1225. 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,Onstott, T.C. (1980) "Application of the Bingham distribution function in paleomagnetic studies". Journal of Geophysical Research, 85:1500–1510. and has been used in the field of computer vision.S. Teller and M. Antone (2000). Automatic recovery of camera positions in Urban Scenes
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. The matrices M and Z are the result of diagonalizing the positive-definite covariance matrix of the Gaussian distribution that underlies the Bingham distribution.
See also Directional statistics von Mises–Fisher distribution Kent distribution
References