kent.mle: MLE of the Kent distribution

In Directional: A Collection of Functions for Directional Data Analysis

MLE of the Kent distribution

Description

MLE of the Kent distribution.

Usage

kent.mle(x)

Arguments

x	A matrix containing spherical data in Euclidean coordinates.

Details

The Kent distribution is fitted to some data and its parameters are estimated. If the normalizing constant cannot be evaluated exactly using Kent's (1982) formula, the saddlepoint approximation of Kume and Wood (2005) is used.

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, either using Kent's (1982) formula or using the third type saddlepoint approximation (Kume and Wood, 2005).
loglik	The value of the log-likelihood.

Author(s)

Michail Tsagris.

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

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.logcon, 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)

Directional documentation built on Oct. 28, 2026, 5:08 p.m.