Bingham distribution
Encyclopedia
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
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
, the Bingham distribution, named after Christopher Bingham
Christopher Bingham
Christopher Bingham is an American statistician who introduced the Bingham distribution. In joint work with C. M. D. Godfrey and John Tukey he introduced complex demodulation into the analysis of time series.-External links:* faculty web page...
, is an antipodally symmetric probability distribution
Probability distribution
In probability theory, a probability mass, probability density, or probability distribution is a function that describes the probability of a random variable taking certain values....
on the n-sphere
Hypersphere
In mathematics, an n-sphere is a generalization of the surface of an ordinary sphere to arbitrary dimension. For any natural number n, an n-sphere of radius r is defined as the set of points in -dimensional Euclidean space which are at distance r from a central point, where the radius r may be any...
. It is widely used in paleomagnetic data analysis.
Its probability density function
Probability density function
In probability theory, a probability density function , or density of a continuous random variable is a function that describes the relative likelihood for this random variable to occur at a given point. The probability for the random variable to fall within a particular region is given by the...
is given by
-
which may also be written-
where x is an axis, M is an orthogonalOrthogonal matrixIn linear algebra, an orthogonal matrix , is a square matrix with real entries whose columns and rows are orthogonal unit vectors ....
orientation matrix, Z is a diagonal concentration matrix,
is a confluent hypergeometric functionConfluent hypergeometric functionIn mathematics, a confluent hypergeometric function is a solution of a confluent hypergeometric equation, which is a degenerate form of a hypergeometric differential equation where two of the three regular singularities merge into an irregular singularity...
of matrix argument.
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