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 FisherâÂÂBingham distributions.
The Bingham distribution is widely used in paleomagnetic data analysis, and has been used 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.