MLe of the Kent distribution

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Description

It estimates the concentration and the ovalness parameter of some directional data assuming the Kent distribution. The mean direction and major and minor axes are also estimated.

Usage

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Arguments

x

A matrix containing spherical data; in Euclidean coordinates.

Details

The Kent distribution is fitted to some data and its parameters are estimated.

Value

A list including:

runtime

The run time of the procedure.

G

A 3 x 3 matrix whose first column is the mean direction. The second and third columns are the major and minor axes respectively.

para

The concentration κ and ovalness β parameters are stored here.

logcon

The logarithm of the normalising constant, using the third type apprxoimation.

loglik

The value of the log-likelihood.

Author(s)

Michail Tsagris

R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Giorgos Athineou <athineou@csd.uoc.gr>

References

Kent John (1982). The Fisher-Bingham distribution on the sphere. Journal of the Royal Statistical Society, Series B, 44(1): 71-80.

See Also

kent.mle, fb.saddle, vmf, wood.mle

Examples

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x <- rvmf(200, rnorm(3), 15)
kent.mle(x)
vmf(x)
A <- diag( c(-5, 0, 5) )
x <- rfb(200, 15, rnorm(3), A)
kent.mle(x)
vmf(x)

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