Bingham distribution

Bingham distribution

In statistics, the Bingham distribution, named after Christopher Bingham, is an antipodally symmetric probability distribution on the "n"-sphere. It is widely used in paleomagnetic data analysis.

Its probability density function is given by

: f(mathbf{x},;,M,Z); dS^{n-1} ;=; {}_{1}F_{1}({ extstylefrac{1}{2;{ extstylefrac{n}{2;Z)^{-1};cdot; expleft({ extrm{tr}; Z M^{T}mathbf{x} mathbf{x}^{T}M} ight); dS^{n-1}

where x is an axis, "M" is an orthogonal orientation matrix, "Z" is a diagonal concentration matrix, {}_{1}F_{1}(cdot;cdot,cdot) is a confluent hypergeometric function of matrix argument.

ee also

* Directional statistics

References

* Bingham, Ch. (1974) "An antipodally symmetric distribution on the sphere". "Annals of Statistics", 2:1201–1225.

* Onstott, T.C. (1980) "Application of the Bingham distribution function in paleomagnetic studies". "Journal of Geophysical Research", 85:1500–1510.


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