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Multivariate Skew Normal distribution

5 messages · Caio Lucidius Naberezny Azevedo, (Ted Harding), Kjetil Halvorsen +2 more

Original
(Ted Harding)
#
On 01-Sep-05 Caio Lucidius Naberezny Azevedo wrote:
Hello, Caio

Please tell us what you mean by "skew normal distribution".

Since normal (i.e. gaussian) distributions are not skew, you
presumably mean something different from what you said, so
unless we understand this more clearly  it is unlikely that
anyone can make a suggestion which would meet your needs.

With best wishes,
Ted.


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E-Mail: (Ted Harding) <Ted.Harding at nessie.mcc.ac.uk>
Fax-to-email: +44 (0)870 094 0861
Date: 01-Sep-05                                       Time: 15:02:37
------------------------------ XFMail ------------------------------
Kjetil Halvorsen
#
(Ted Harding) wrote:

            

      
      
      
    

        
Well, but then somebody (Azzalini?) coined the term skew-normal, which 
you can
read about at    http://azzalini.stat.unipd.it//SN
or simply do
library(help=sn) # after installing from CRAN.
This family is obtained by skewing a normal family, hence the name.
You can also skew a t -family or whatever other symmetric family you like.

I found this usefull for modelling.

Kjetil

            

      
      
      
    

        

      
      
    

        
-- 

Kjetil Halvorsen.

Peace is the most effective weapon of mass construction.
               --  Mahdi Elmandjra

  
    

      
      
    

  


  


      

    

    

      
      

        


  

        

      David Scott
    

    

      
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On Thu, 1 Sep 2005 Ted.Harding at nessie.mcc.ac.uk wrote:

        

            

      
      
      
    

        
Actually Ted it is perfectly clear. There are modifications of the normal 
(more than one approach) which incorporate skewness.

There is a very nice package by Azzellini called sn which deals with this 
and with the skew t.

A different version of the skew t is given in the package skewt. This is 
univariate only.

There also appear to be some skew normal and skew t tools in RMetrics (in 
FSeries and fPortfolio).

What is not clear is why Caio keeps asking the same question when I 
emailed him the name of the package yesterday.

David Scott
_________________________________________________________________
David Scott	Department of Statistics, Tamaki Campus
 		The University of Auckland, PB 92019
 		Auckland	NEW ZEALAND
Phone: +64 9 373 7599 ext 86830		Fax: +64 9 373 7000
Email:	d.scott at auckland.ac.nz


Graduate Officer, Department of Statistics

  
  


  


      

    

    
3 days later

    

      
      

        


  

        

      Adelchi Azzalini
    

    

      
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On Thu, 1 Sep 2005 13:09:00 +0000 (GMT), Caio Lucidius Naberezny

        
Azevedo wrote:

        
CLNA> 
CLNA>  Could anyone tell me if there is any package (or function) that
CLNA>  generates values from a multivariate skew normal distribution?

try the following

library(sn)
location <- c(20,4) # e.g. for a two-dimensional variable
dispers  <- matrix(c(3,-2,-2,2), 2,2)
skew <- c(10,-6)
rmsn(n=10, xi=location, Omega=dispers, alpha=skew) # for skew-normal data
rmst(n=10, xi=location, Omega=dispers, alpha=skew, df=5) # for skew-t data

see also help(rsn) and help(rst) for the univariate case

for more information, see also (as already pointed out in the list):
  http://azzalini.stat.unipd.it/SN

best wishes,
Adelchi Azzalini