Re: Multivariate student t: normalization in mvtrnd

[Arno Onken]

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