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 mtsagris@uoc.gr and Giorgos Athineou <gioathineou@gmail.com>.
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