Directional statistics | Continuous distributions

Bingham distribution

In statistics, the Bingham distribution, named after Christopher Bingham, is an antipodally symmetric probability distribution on the n-sphere. 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, and has been reported as being of use in the field of computer vision. 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. (Wikipedia).

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Related pages

Orthogonal matrix | Kent distribution | Multivariate normal distribution | Hypergeometric function of a matrix argument | Diagonalizable matrix | Directional statistics | Statistics | Probability distribution | Probability density function | Von Mises–Fisher distribution