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Re: Multivariate student t: normalization in mvtrnd


From: Iñigo Urteaga
Subject: Re: Multivariate student t: normalization in mvtrnd
Date: Wed, 28 Nov 2012 11:11:25 -0500

Hi Arno,

Thank you for your reply. If you don't mind, I would like to clarify a
couple of points, so that we can include them in the help for the sake
of clarity:

> Well, it's not hard to rescale the result of mvtrnd to get an arbitrary
> covariance matrix. You might also want to add a constant to get a
> non-zero mean. In contrast to mvnrnd, mvtrnd doesn't have arguments for
> that.

Yes, adding a non-zero mean is trivial, but how would you rescale the
result of mvtrnd to get an arbitrary covariance matrix? That is, if a
a covariance matrix V is provided, which is normalized by mvtrnd to
the correlation matrix R=V./(sqrt(diag(V)*diag(V))), then what is the
resulting covariance of the obtained samples in terms of V?

> mvtrnd just gives you the equivalent of the standard normal.

As far I understand it, mvtrnd provides the standard student t
distribution only when the provided correlation matrix R is the
Identity matrix. For the rest of cases when R is not the identity
matrix, the resulting samples are not distributed according to the
standard t, am I right?

Thank you again,

Iñigo

On Wed, Nov 28, 2012 at 5:06 AM, Arno Onken <address@hidden> wrote:
> Hi Iñigo,
>
> On 11/28/12 01:12, Iñigo Urteaga wrote:
>> Thanks a lot for clarifying that Octave's mvtrnd normalizes the
>> covariance matrix into the correlation matrix just for compatibility
>> purposes with Matlab. I understand that this is design criteria and I
>> don't expect it to change. Nevertheless, what is the reasoning behind
>> not using the covariance but the correlation matrix? Is there any
>> advantage?
>
> Well, it's not hard to rescale the result of mvtrnd to get an arbitrary
> covariance matrix. You might also want to add a constant to get a
> non-zero mean. In contrast to mvnrnd, mvtrnd doesn't have arguments for
> that. mvtrnd just gives you the equivalent of the standard normal. So
> the advantage is conceptual. I think it is good to have compatibility at
> this point.
>
>> Finally, would it make any sense to expand mvtrnd's help a little to
>> clarify this point for other users? I spent some time trying to figure
>> this out, so I consider it might be helpful for others. If you agree,
>> I am willing to help.
>
> Yes, that's definitely a good idea. You are welcome to help.
>
> Arno


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