Directional (version 6.8)

MLE of the Kent distribution: MLe of the Kent distribution

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

kent.mle(x)

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.

param

A vector with the concentration \(\kappa\) and ovalness \(\beta\) parameters and the angle \(\psi\) used to rotate H and hence estimate G as in Kent (1982).

logcon

The logarithm of the normalising constant, using the third type approximation (Kume and Wood, 2005).

loglik

The value of the log-likelihood.

Arguments

x

A matrix containing spherical data in Euclidean coordinates.

Author

Michail Tsagris.

R implementation and documentation: Michail Tsagris and Giorgos Athineou <[e-mail]>.

Details

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

References

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

Kume Alfred and Wood Andrew T.A. (2005). Saddlepoint approximations for the Bingham and Fisher-Bingham normalizing constants. Biometrika, 92(2):465--476

See Also

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

Examples

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