jrogers at cantatapharm.com
Sun Oct 6 02:33:48 CEST 2002
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...
From: Timo Mäkeläinen [mailto:Timo.Makelainen at Helsinki.fi]
Sent: Sat 10/5/2002 1:52 AM
To: Jim Rogers
Subject: Re: [R] T-Distribution
On 4 Oct 2002, at 9:02, Jim Rogers wrote:
> Roger Koeneker wrote:
> > rmvt <- function(corr,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.
> James A. Rogers <rogers at cantatapharm.com>
> Statistical Scientist
> Cantata Pharmaceuticals
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