MLE of the SESPC distribution {Directional}

MLE of the SESPC distribution

Description

MLE of the SESPC distribution.

Usage

sespc.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, set this equal to TRUE. Otherwise leave it FALSE.

tol

A tolerance value to stop performing successive optimizations.

Details

MLE of the SESPC distribution is implemented. SESPC stands for Spherical Elliptically Symmetric Projected Cauchy and it was suugested by Tsagris and Alzeley (2023). Unlike the spherical independent projected Cauchy distribution this is rotationally symmetric and is a competitor of the spherical ESAG and Kent distributions (which are also ellitpically symmetric).

Value

A list including:

mu

The mean vector in R^3.

theta

The two \theta parameters.

loglik

The log-likelihood value.

vinv

The inverse of the covariance matrix. It is returned if the argument "full" is TRUE.

lambda

The \lambda_2 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.

sipc.loglik

The log-likelihood value of the isotropic prohected Cuchy distribution, which is rotationally symmetric.

Author(s)

Michail Tsagris.

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

References

Tsagris M. and Alzeley O. (2023). Circular and spherical projected Cauchy distributions: A Novel Framework for Circular and Directional Data Modeling. https://arxiv.org/pdf/2302.02468.pdf

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

See Also

dsespc, rsespc, sipc.mle, esag.mle, spher.sespc.contour

Examples

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