dmvsnorm & mvst in fMultivar

[Adelchi Azzalini]

Dear Colleagues,

I am writing about some functions incorporated into your package
"fMultivar", specifically dmvsnorm & mvst, which originate from 
packages 'sn'. In principle, it is welcome that your package
incorporates some routines from my package. Unfortunately, this
operation has been done improperly, and the effect is seriously
misleading for the user.

In the documentation of the above-mentioned functions, one reads:

mu, Omega, alpha, df: [*mvsnorm][*mvst] - 
           the model parameters: 
           'mu' a vector of mean values, one for each column, 
           'Omega' the covariance matrix, 
           'alpha' the skewness vector, and 
           'df' the number of degrees of freedom which is a measure for
          the fatness of the tails (excess kurtosis). 

and in the code mu is set equal to xi, which is a location parameter,
but _not_ the mean, as the documentation wrongly indicates. In fact 
in the skew-t case the mean may even not exist. Similarly, Omega is 
described as "the covariance matrix", which suggests that this is
the covariance matrix of the distribution, but it is not true.
Omega is _a_ covariance matrix, which is related to the covariance
matrix (when this one exists) but it is different. For the
parametrization based on mean and variance, see later.

In addition, in the code of dmvsnorm, for the one-dimensional case
there is the assignment

 ans = dsn(x, location = xi[1], scale = as.vector(Omega)[1], 
           shape = alpha[1])

which is wrong since in this case the scale is the square root of
Omega. Similar errors exist in pmvsnorm, dmvst, pmvst.

Please note that the above remarks do not attempt to be exhaustive,
since I have not done a full scan of your code and documentation.
These are just the problems which I have spotted after a quick
browsing of your package.

I take this opportunity to draw your attention to this note:
   http://tango.stat.unipd.it/SN/announce2.html
When the new "version 1.xx" will be available, it will include
a parametrization based on mean/variance.

With best wishes,

Adelchi Azzalini  

-- 
Adelchi Azzalini  <azzalini at stat.unipd.it>
Dipart.Scienze Statistiche, Università di Padova, Italia
tel. +39 049 8274147,  http://azzalini.stat.unipd.it/