MLE of the SESPC distribution.
sespc.mle(y, full = FALSE, tol = 1e-06)A list including:
The mean vector in \(R^3\).
The two \(\theta\) parameters.
The log-likelihood value.
The inverse of the covariance matrix. It is returned if the argument "full" is TRUE.
The \(\lambda_2\) parameter (smallest eigenvalue of the covariance matrix). It is returned if the argument "full" is TRUE.
The angle of rotation \(\psi\) set this equal to TRUE. It is returned if the argument "full" is TRUE.
The log-likelihood value of the isotropic prohected Cuchy distribution, which is rotationally symmetric.
A matrix with the data expressed in Euclidean coordinates, i.e. unit vectors.
If you want some extra information, the inverse of the covariance matrix, set this equal to TRUE. Otherwise leave it FALSE.
A tolerance value to stop performing successive optimizations.
Michail Tsagris.
R implementation and documentation: Michail Tsagris mtsagris@uoc.gr.
MLE of the SESPC distribution is implemented. SESPC stands for Spherical Elliptically Symmetric Projected Cauchy and it was suugested by Tsagris and Alzeley (2024). 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).
Tsagris M. and Alzeley O. (2024). Circular and spherical projected Cauchy distributions: A Novel Framework for Circular and Directional Data Modeling. Australian & New Zealand Journal of Statistics (accepted for publication). https://arxiv.org/pdf/2302.02468.pdf
Mardia K. V. and Jupp P. E. (2000). Directional statistics. Chicester: John Wiley & Sons.
dsespc, rsespc, sipc.mle, esag.mle, spher.sespc.contour
m <- colMeans( as.matrix( iris[,1:3] ) )
y <- rsespc(1000, m, c(1,0.5) )
sespc.mle(y)
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