Directional (version 3.1)

MLE of the ESAG distribution: MLE of the ESAG distribution

Description

MLE of the ESAG distribution.

Usage

ESAGmle(y, tol = 1e-07)

Arguments

y

A matrix with the data expressed in Euclidean coordinates, i.e. unit vectors.

tol

The tolerance to accept that the E-M algorithm used to estimate the concentration parameter has converged.

Value

A list including:

mu

The mean vector in \(R^3\).

gam

The two gamma parameters.

loglik

The log-likelihood value.

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

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

Paine P.J., Preston S.P., Tsagris M. and Wood A.T.A. (2017). An Elliptically Symmetric Angular Gaussian Distribution. Statistics and Computing (To appear).

See Also

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

Examples

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