esag.mle: MLE of the ESAG distribution

In Directional: A Collection of Functions for Directional Data Analysis

MLE of the ESAG distribution

Description

MLE of the ESAG distribution.

Usage

esag.mle(y, full = FALSE, tol = 1e-06)

Arguments

y	A matrix with the data expressed in Euclidean coordinates, i.e. unit vectors.
full	If you want some extra information, the inverse of the covariance matrix, the rho parameter (smallest eigenvalue of the covariance matrix) and the angle of rotation \psi, set this equal to TRUE. Otherwise leave it FALSE.
tol	A tolerance value to stop performing successive optimizations.

Details

MLE of the MLE of the ESAG distributiontribution, on the sphere, is implemented. ESAG stands for Elliptically Symmetric Angular Gaussian and it was suugested by Paine et al. (2018). Unlike the projected normal distribution this is rotationally symmetric and is a competitor of the spherical Kent distribution (which is also elliptically symmetric).

Value

A list including:

mu	The mean vector in R^3.
gam	The two \gamma parameters.
loglik	The log-likelihood value.
vinv	The inverse of the covariance matrix. It is returned if the argument "full" is TRUE.
rho	The rho parameter (smallest eigenvalue of the covariance matrix). It is returned if the argument "full" is TRUE.
psi	The angle of rotation \psi set this equal to TRUE. It is returned if the argument "full" is TRUE.
iag.loglik	The log-likelihood value of the isotropic angular Gaussian distribution. That is, the projected normal distribution which is rotational symmetric.

Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris [e-mail].

References

Paine P.J., Preston S.P., Tsagris M. and Wood A.T.A. (2018). An Elliptically Symmetric Angular Gaussian Distribution. Statistics and Computing, 28(3):689–697.

Mardia, K. V. and Jupp, P. E. (2000). Directional statistics. Chicester: John Wiley & Sons.

See Also

desag, resag, iag.mle, kent.mle, acg.mle, circ.summary, sphereplot

Examples

m <- colMeans( as.matrix( iris[,1:3] ) )
y <- resag(1000, m, c(1,0.5) )
esag.mle(y)

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