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Re: Multivariate student t: normalization in mvtrnd
From: |
Arno Onken |
Subject: |
Re: Multivariate student t: normalization in mvtrnd |
Date: |
Thu, 29 Nov 2012 22:13:30 +0100 |
User-agent: |
Mozilla/5.0 (X11; Linux x86_64; rv:10.0.11) Gecko/20121122 Icedove/10.0.11 |
Hi Iñigo,
On 11/29/12 16:49, Iñigo Urteaga wrote:
> Thank you for your clarifying response. Based on our discussion, here
> are my proposed lines for the mvtrnd help:
>
> ----------------
> Usage tips
> ----------------
>
> The argument SIGMA provided must be the correlation matrix and, if
> not, it is normalized so that the resulting covariance of the obtained
> samples follows:
>
> cov(samples) = nu/(nu-2) * SIGMA./(sqrt(diag(SIGMA)*diag(SIGMA)))
>
> In order to obtain samples distributed according to an standard
> multivariate student's t, the correlation matrix must be equal to the
> identity matrix I of dimension n ( mvtrnd(eye(n),nu,M) ).
>
> Therefore, to generate multivariate student's t samples with arbitrary
> covariance matrix V, any of the following scaling might be used:
>
> (1) samples = diag(sqrt(diag(V))) * mvtrnd (V, nu, M)'
> (2) samples = chol(V)' * mvtrnd(eye(n),nu,M)'
>
> ----------------
>
> Let me know your opinion on this and, once again, thanks a lot for all
> the support.
Your help text sounds great. It clarifies the arguments considerably.
Thanks a lot! I will include the text in mvtrnd.
Thanks,
Arno