\name{Mixtures of elliptically symmetric distributions}
\alias{mixsespc.mle}
\alias{mixesag.mle}
\title{
Mixtures of elliptically symmetric distributions
}

\description{
It performs model based clustering for spherical data assuming ellitpically symetric distributions.
}

\usage{
mixsespc.mle(x, g = 2, tol = 1e-4)
mixesag.mle(x, g = 2, tol = 1e-4)
}

\arguments{
\item{x}{
A matrix with the data expressed as unit vectors.
}
\item{g}{
The number of groups to fit. It must be greater than or equal to 2.
}
\item{tol}{
The tolerance value to terminate the EM algorithm.
}
}

\details{
The functions performs model-based clustering using mixtures of SESPC or mixtures
of ESAG distributions. The initial step of the algorithm is based on a Gaussian mixture model.
}

\value{
A list including:
\item{param}{
A matrix with the mean direction, the concentration parameters and mixing probability of each group.
}
\item{loglik}{
The value of the maximised log-likelihood.
}
\item{probs}{
The estimated probabilities of each observation to belong to each cluster.
}
\item{pred}{
The predicted group of each observation.
}
\item{iter}{
The number of iteration required by the EM algorithm.
}
\item{runtime}{
The run time of the algorithm. A numeric vector. The first element is the user time, the second element is the system time and the third element is the elapsed time.
}
}

\references{
Perdikis T., Alharbi N. and Tsagris M. (2026). Model--based clustering for spherical
and hyper--spherical data using elliptically symmetric distributions.

https://arxiv.org/abs/2605.27496
}

\author{
Michail Tsagris and Theodoros Perdikis.

R implementation and documentation: Michail Tsagris \email{mtsagris@uoc.gr}.
}
%\note{
%%  ~~further notes~~
%}
\seealso{
\code{\link{bic.mixsespc}
}
}

\examples{
x <- as.matrix( iris[, 1:3] )
x <- x / sqrt( rowSums(x^2) )
mixsespc.mle(x)
}
