# kent.mle: MLe of the Kent distribution In Directional: A Collection of Functions for Directional Data Analysis

 MLE of the Kent distribution R Documentation

## 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)


### 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. 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.

### Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris mtsagris@uoc.gr and Giorgos Athineou <gioathineou@gmail.com>.

### 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

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)


Directional documentation built on Oct. 12, 2023, 1:07 a.m.