Directional (version 4.0)

MLE of the ESAG distribution: MLE of the ESAG distribution

Description

MLE of the ESAG distribution.

Usage

ESAGmle(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.

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.

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. (2017). Unlike the projected normal distribution this is rotationally symmetric and is a competitor of the spherical Kent distribution (which is also non rotational symmetric).

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

ESAGdensity, ESAGsim, iag.mle, kent.mle, acg, circ.summary, sphereplot

Examples

# NOT RUN {
m <- colMeans( as.matrix( iris[,1:3] ) )
y <- ESAGsim(1000, c(m, 1,0.5) )
ESAGmle(y)
# }