MLE of the ESAG distribution {Directional} | R Documentation |
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 |
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 |
gam |
The two |
loglik |
The log-likelihood value. |
vinv |
The inverse of the covariance matrix. It is returned if the argument "full" is TRUE. |
rho |
The |
psi |
The angle of rotation |
iag.loglik |
The log-likelihood value of the isotropic angular Gaussian distribution. That is, the projected normal distribution which is rotationally symmetric. |
Author(s)
Michail Tsagris.
R implementation and documentation: Michail Tsagris mtsagris@uoc.gr.
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)