T-Distribution

Timo (see below) was kind enough to reply in private that part of my comment was incorrect. 
 
As he points out, the joint distribution of two independent T distributions is NOT a multivariate T distribution in the usual sense. That distinction had not occured to me. 
 
I hope I do more good than harm by trying to learn in public...
 
Jim
 
-----Original Message----- 
From: Timo M?kel?inen [mailto:Timo.Makelainen at Helsinki.fi] 
Sent: Sat 10/5/2002 1:52 AM 
To: Jim Rogers 
Cc: 
Subject: Re: [R] T-Distribution

>
	> >
	> >   rmvt <- function(corr,df)
	> rmvnorm(n,sigma=corr)/sqrt(rchisq(n,df)/df)
	> >
	>
	> That would do the trick.
	>
	> One interesting note relating to Hicham's original question (Hicham
	> was the originator of this thread):
	>
	> The multivariate T distribution does not have elliptical contours. For
	> example, the contours of an independent bivariate T are not circles.
	
	But this differs from common usage (and your formulae above):  the
	multivariate T has dependent components and also ellipsoidal level
	surfaces (Raiffa & Schlaifer 1961, 1968, Section 8.3; there may be
	a problem with subsection 8.3.1, though).
	
	> One of the many fascinating facts about the independent bivariate
	> Normal distribution is that it is the ONLY independent bivariate
	> distribution with circular contours. Many people may know this, but I
	> know it was a surprise to me when I learned it.
	>
	> --Jim
	>
	> James A. Rogers <rogers at cantatapharm.com>
	> Statistical Scientist
	> Cantata Pharmaceuticals
	>
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	Best wishes,
	
	Timo
	
	
	Timo Makelainen, Department of Mathematics
	University of Helsinki, P.O. Box 4
	FIN-00014 Helsinki
	Tel.: +358-9-19122863
	Fax:  +358-9-19123213
	E-mail: Timo.Makelainen at Helsinki.Fi
	


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