The sn package provides facilities to define and manipulate probability distributions of the skew-normal (SN) family and some related ones, notably the skew-t (ST) family, and to apply connected statistical methods for data fitting and diagnostics, in the univariate and the multivariate case.
The first version of the package was written in 1997 (on CRAN since 1998); subsequent versions have evolved gradually up to version 0.4-18 in May 2013. In January 2014, version 1.0-0 has been uploaded to CRAN; this represented a substantial re-writing of the earlier ‘version 0.x’. Differences between the ‘version 0’ and the ‘version 1’ series are radical; they concern the core computational and graphical part as well as the user interface. Since version 1.0-0, the S4 protocol for classes and methods has been adopted.
Broadly speaking, the available tools can be divided in two groups: the
probability section and the statistics section. For a quick start, one
could look at their key functions,
selm, respectively, and from here explore the rest.
In the probability section, one finds also functions
dmsn and others alike; these functions
existed also in ‘version 0’ and their working is still very much
the same (not necessarily so their code). Additional information
on the current package structure and the set of commands is available in a
overview of the package.
The first instance of the ‘version 1’ series (that is, 1.0-0) has appeared at the same time when the companion book by Azzalini and Capitanio (2014) was published. Although the two projects are formally separate, they adopt the same notation, terminology and logical frame. This matching and the numerous references in the software documentation to specific sections of the book for background information should facilitate familiarizing with these tools.
Information on additional and on more recent change to the package is
NEWS file, accessible from the package documentation
A word of explanation is appropriate about the numerous references to Azzalini and Capitanio (2014) in the documentation of the package. The reason why the documentation often refers to the monograph rather than to the original research papers is that the book provides a relatively informal summary of material which has been elaborated in a number of technical papers, sometimes very technical or with information on the point of interest mixed with other material. In other words, the motivation behind this policy is readability, not indulgence in self-citation. When one or a few original sources appeared to deliver the required information in a compact and accessible form, they have been cited directly. In any case, the quoted sections of the book include bibliographic notes which refer back to the original sources.
There is a partial backward compatibility of ‘version 1.x-y’ versus
Some functions of the older version would work as before
with virtually no change; a wider set arguments is now allowed. Functions
dmsn and alike fall in
this category: in some cases, the names of the arguments have been altered,
but they work as before if called with unnamed arguments; similar cases are
Notice, however, that
msn.mle and other fitting functions have
effectively been subsumed into the more comprehensive fitting function
A second group of functions will work with little or even minimal changes.
Specific examples are functions
st.mle which have
st.mple, with some additional
arguments (again, one can achieve the same result via
Another example is constitude by the group of functions
st.cumulants.inversion, which have been replaced
by the more general functions
one only needs to pay attention to conversion from 3rd and 4th order
cumulants to their standardized form in connection with the replacement of
Finally, some functions are not there any longer, with no similarly-working
functions in the new version. This is the case of
st.mle.grouped for maximum likelihood estimation from
grouped data, that is, data recorded as intervals and corresponding
R version 2.15-3 or higher, plus packages mnormt, numDeriv, stats4 in addition to standard packages (methods, graphics, etc.)
citation("sn") indicates, among other information,
the running version of the package.
The most recent version of the package can be obtained from
the web page: http://azzalini.stat.unipd.it/SN
which also provides related material.
From the above-indicated web page, one can also obtain the package ‘sn0’ which is essentially the last ‘version 0’ (that is, 0.4-18) with suitable renaming of certain ingredients. This allows to have both the current and the old package installed at the same time.
Adelchi Azzalini. Please send comments, error reports et cetera to the author, whose web page is http://azzalini.stat.unipd.it/.
This package and its documentation are usable under the terms of the “GNU General Public License” version 3 or version 2, as you prefer; a copy of them is available from https://www.R-project.org/Licenses/.
While the software is freely usable, it would be appreciated
if a reference is inserted in publications or other work
which makes use of it. For the appropriate way of referencing it,
see the command
Azzalini, A. with the collaboration of Capitanio, A. (2014). The Skew-Normal and Related Families. Cambridge University Press, IMS Monographs series.
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