%  file sn/man/summary.SECdistr.Rd  
%  This file is a component of the package 'sn' for R
%  copyright (C) 2013-2015 Adelchi Azzalini
%---------------------
\name{summary.SECdistr}
\alias{summary.SECdistr}
\alias{summary.SECdistrUv}
\alias{summary.SECdistrMv}
\alias{summary,SECdistrUv-method}
\alias{summary,SECdistrMv-method}

\title{Summary of a \acronym{SEC} distribution object}

\description{Produce a summary of an object of class either
\code{"SECdistrUv"} or \code{"SECdistrMv"}, which refer to a univariate or a
multivariate \acronym{SEC} distribution, respectively. Both types of
objects can be produced by \code{makeSECditr}. }

\usage{
\S4method{summary}{SECdistrUv}(object, cp.type = "auto", probs)

\S4method{summary}{SECdistrMv}(object, cp.type = "auto")
}

\arguments{
  \item{object}{an object of class \code{"SECdistrUv"} or \code{"SECdistrMv"}.}

  \item{cp.type}{a character string to select the required variance of
    \acronym{CP} parameterization; possible values are \code{"proper"},
    \code{"pseudo"}, \code{"auto"} (default). For a description of these
    codes, see \code{\link{dp2cp}}.}
  
 \item{probs}{in the univariate case, a vector of probabilities for which 
    the corresponding quantiles are required. If missing, the vector
     \code{c(0.05, 0.25, 0.50, 0.75, 0.95)} is used.}
}

%\details{%%  ~~ If necessary, more details than the description above ~~}

\value{A list with the following components:
  \item{family}{name of the family within the \acronym{SEC} class, character}
  \item{dp}{\acronym{DP} parameters, a list or a vector}
  \item{name}{the name of the distribution, character string}
  \item{compNames}{in the multivariate case the names of the components,
     a character vector}
  \item{cp}{\acronym{CP} parameters, a list or a vector}
  \item{cp.type}{the name of the selected variant of the \acronym{CP} set}
  \item{aux}{a list with auxiliary ingredients (mode, coefficients of 
       skewness and kurtosis, in the parametric and non-parametric variants, 
       and more).}
       
\acronym{DP} and \acronym{CP} are vectors if \code{class(object)} is  
\code{SECdistrUv} (univariate distribution); they are lists if code{class(object)} is  \code{SECdistrMv} (multivariate distribution). 
The examples below show how extract components from \code{aux} and other slots. 
}
 
\author{Adelchi Azzalini}

%\note{%%  ~~further notes~~}

%% ~Make other sections like Warning with \section{Warning }{....} ~

\seealso{\code{\link{makeSECdistr}} for extracting a \acronym{SEC}
 distribution from a \code{\link{selm}} fit 
 
 methods \code{\link[base]{mean}} and \code{\link[stats]{vcov}} 
 for computing the mean (vector) and the variance (matrix) of 
 \code{\link{SECdistrUv-class}} and \code{\link{SECdistrMv-class}} objects
 }

\examples{
f3 <- makeSECdistr(dp=c(3,2,5), family="SC")
summary(f3)
s <- summary(f3, probs=(1:9)/10)
print(slotNames(s)) 
print(names(slot(s,"aux")))   # the components of the 'aux' slot
slot(s, "aux")$mode           # the same of modeSECdistr(object=f3)
slot(s, "aux")$q.measures     # quantile-based measures of skewness and kurtosis
#
dp3 <- list(xi=1:3, Omega=toeplitz(1/(1:3)), alpha=c(-3, 8, 5), nu=6)
st3 <- makeSECdistr(dp=dp3, family="ST", compNames=c("U", "V", "W"))
s <- summary(st3)
dp <- slot(s, "dp")           # the same of slot(st3, "dp")
slot(s, "cp")$var.cov         # the same of vcov(st3)
slot(s, "aux")$delta.star     # comprehensive coefficient of shape
slot(s, "aux")$mardia         # Mardia's measures of asymmetry and kurtosis
#
dp2 <- list(xi=rep(0,2), Omega=matrix(c(2,2,2,4),2,2), alpha=c(3,-5), tau=-1)
esn2 <- makeSECdistr(dp=dp2, family="ESN", name="ESN-2d")
summary(esn2)
}
\keyword{multivariate}
\keyword{distribution}