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% This file is a component of the package 'sn' for R
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% copyright (C) 2013 Adelchi Azzalini
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\title{Package `sn': summary information}
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\concept{skew-elliptical distribution}
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\concept{skew-normal distribution}
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\title{Package \pkg{sn}: overview}
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This package provides functions related to the skew-normal (SN) and
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the skew-t (ST) probability distributions, both for the univariate
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and for the the multivariate case, including regression models.
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% The functions of the scalar case section are:
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% \code{dsn}, \code{psn}, \code{qsn}, \code{rsn}, \code{T.Owen},
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% \code{cp.to.dp}, \code{dp.to.cp}, \code{zeta},
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% \code{gamma1.to.lambda}, \code{sn.cumulants}, \code{sn.em},
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% \code{sn.2logL.profile}, \code{sn.mle}, \code{sn.dev},
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% The functions of the multivariate section are: \code{dmsn},
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% \code{rmsn}, \code{plot.dsn2}, \code{msn.quantities},
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% \code{msn.conditional}, \code{msn.marginal}, \code{plot.msn.cond},
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% \code{msn.fit}, \code{msn.mle}, \code{msn.dev}, \code{msn.dev.grad},
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% \code{msn.moment.fit}, \code{num.deriv}.
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The package includes several functions, a number of which are intended
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as services to other functions, not really to be called directly by the
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users. The following ones are those more relevant for practical use.
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\emph{SN distribution:}
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\code{\link{dsn}}, \code{\link{psn}}, \code{\link{qsn}},
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\code{\link{rsn}}, \code{\link{cp.to.dp}}, \code{\link{dp.to.cp}},
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\code{\link{sn.mle}}, \code{\link{sn.em}},
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%\code{\link{sn.mle.grouped}}
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for the univariate case, and
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\code{\link{dmsn}}, \code{\link{pmsn}}, \code{\link{rmsn}},
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\code{\link{msn.fit}}, \code{\link{msn.mle}}, \code{\link{dsn2.plot}}
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for the multivariate case.
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\emph{ST distribution:}
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\code{\link{dst}}, \code{\link{pst}}, \code{\link{rst}}, \code{\link{st.mle}},
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%\code{\link{st.mle.grouped}}
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for the univariate case,
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and \code{\link{dmst}},\code{\link{pmst}}, \code{\link{rmst}},
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\code{\link{mst.fit}}, \code{\link{mst.mle}}, \code{\link{dst2.plot}}
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for the multivariate case.
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It is suggested that a user starts by reading the documentation of
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(some of) these functions.
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The \pkg{sn} package provides facilities to define and manipulate
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probability distributions of the skew-normal (\acronym{SN}) family and
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some related ones, notably the skew-\eqn{t} (\acronym{ST}) family,
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and to apply connected statistical methods for data fitting and
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diagnostics, in the univariate and the multivariate case.
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\section{A substantial upgrade}{The first version of the package has been
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written in 1997 (on CRAN since 1998); subsequent versions have evolved
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gradually up to version 0.4-18 in May 2013. The present \sQuote{version 1}
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of the package is a substantial re-writing of the earlier \sQuote{version 0}.
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Differences between \sQuote{version 0} and \sQuote{version 1} concern the core
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computational and graphical part as well as the user interface.
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The S4 protocol for classes and methods has been adopted.
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Broadly speaking, the available tools can be divided in two groups: the
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probability section and the statistics section. For a quick start, one
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could look at their key functions, \code{\link{makeSECdistr}} and
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\code{\link{selm}}, respectively, and from here explore the rest.
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In the probability section, one finds also functions \code{\link{dsn}},
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\code{\link{dst}}, \code{\link{dmsn}} and others alike; these functions
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existed also in \sQuote{version 0} and their working is still very much
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the same (not necessarily so their code).
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The upgrade to \sQuote{version 1} appears more or less at the time when the
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companion book by Azzalini and Capitanio (2014) is published. Although the two
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projects are formally separate, they adopt the same notation, terminology
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and logical frame. This matching and the numerous references in the software
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documentation to specific sections of the book for background information
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should facilitate familiarizing with these tools.}
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\section{Backward Compatibility}{%
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There is a partial backward compatibility of \sQuote{version 1} versus
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\sQuote{version 0}. Some functions of the older version would work as before
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with virtually no change; a wider set arguments is now allowed. Functions
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\code{\link{dsn}}, \code{\link{dst}}, \code{\link{dmsn}} and alike fall in
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this category: typically, the names of the arguments have been altered, but
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they work as before if called with unnamed arguments; similar cases are
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\code{\link{msn.mle}}, \code{\link{sn.cumulants}} and \code{\link{T.Owen}}.
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Notice, however, that \code{\link{msn.mle}} and other fitting functions have
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effectively been subsumed into the more general fitting function
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A second group of functions will work with little or even minimal changes.
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Specific examples are functions \code{sn.mle} and \code{sn.mle} which have
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become \code{\link{sn.mple}} and \code{\link{st.mple}}, with some additional
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arguments (again, one can achieve the same result via \code{\link{selm}}) and
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\code{dp.to.cp}, which has been replaced by the more general function
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Finally, some functions are not there any longer, with no similarly-working
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functions in the new version. The more prominent set of cases is represented
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by the functions for computing profile log-likelihoods. There is a long-term
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plan to re-instate similar facilities, possibly in a more flexible form, but
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not in the near future. }
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\section{Requirements}{
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A few functions make use of package \code{mnormt}:
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\code{psn}, \code{pmsn}, \code{pmst}.
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\R version 2.15-3 or higher, plus packages \pkg{mnormt},
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\pkg{numDeriv}, \pkg{stats4} and \pkg{methods} in addition to `standard'
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packages (\pkg{graphics}, etc.)
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The version level of the package is given by the command
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\code{print(.sn.version)}.
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The command \code{citation("sn")} indicates, among other information,
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the running version of the package.
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The most recent version of the package can be obtained from
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the WWW page: \url{http://azzalini.stat.unipd.it/SN}
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which also contains other related material
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which also contains other related material.
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Adelchi Azzalini, Dipart. Scienze Statistiche, Universit� di Padova, Italia.
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Please send comments, error reports, etc. to the author whose WWW page
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\section{Author}{Adelchi Azzalini.
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% Dipart. Scienze Statistiche, Università di Padova, Italia.
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Please send comments, error reports, etc. to the author whose web page
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is \url{http://azzalini.stat.unipd.it/}.
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This package and its documentation are usable under the terms of the
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"GNU General Public License", a copy of which is distributed with the
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package. While the software is freely usable, it would be appreciated
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This package and its documentation are usable under the terms of
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the \dQuote{GNU General Public License} version 3 or version 2,
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as you prefer; a copy of them is available from
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\url{http://www.R-project.org/Licenses/}.
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While the software is freely usable, it would be appreciated
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if a reference is inserted in publications or other work
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which makes use of it; for this purpose, see the command
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\code{citation("sn")}.
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\section{Acknowledgements}{The package has evolved through several
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versions, developed over some years.
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For versions up to 0.20, the following people and institutions
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have contributed. Many thanks go to Antonella Capitanio for testing
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the procedures, and to Brian Ripley, Kurt Hornik and Martin Maechler
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for useful advice on R.
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The function \code{num.deriv2} is based on a similar
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function written by Monica Chiogna. The first version of this software
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and part of the associated theoretical work has been developed
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while the author was at the Nuffield College, Oxford, under the Jemolo
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Fellowship scheme; the generous support of the college is gratefully
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Additional support for the development of the theoretical research work has
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been provided by the "Consiglio Nazionale delle Ricerche" of Italy, grant
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Versions 0.21 to 0.30 have been supported by "MIUR", Italy, under grant
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scheme PRIN 2000. Again, thanks to Antonella Capitanio for additional
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testing of those versions of the package.
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Azzalini, A. with the collaboration of Capitanio, A. (2014).
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\emph{The Skew-Normal and Related Families}.
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Cambridge University Press, IMS Monographs series.
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\keyword{multivariate}
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\keyword{distribution}
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\keyword{regression}
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man/sn.Rd
