esag.mle: MLE of the ESAG distribution

Description Usage Arguments Details Value Author(s) References See Also Examples

View source: R/esag.mle.R

Description

MLE of the ESAG distribution.

Usage

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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 ψ 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. (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).

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 ψ 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 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

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

Directional documentation built on Nov. 8, 2021, 1:07 a.m.