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Bingham distribution

Antipodally symmetric probability distribution on the n-sphere From Wikipedia, the free encyclopedia

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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 used 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. The matrices M and Z are the result of diagonalizing the positive-definite covariance matrix of the Gaussian distribution that underlies the Bingham distribution.

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References

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