I have some data for a multivariate normal distribution. It is:

The mean of each of the marginal distributions. mu1, mu2, ... , mun: in vectormu

The 99th percentile for each of the marginal distributions. VaR1, VaR2, ..., VaRn: in vectorVaR

The correlation matrix between each of the marginal distributions.sigma

From this information I am able to calculate the standard deviation for each of the marginal distributions. sd1, sd2, ..., sdn: in vectorsd

Then calculate the mean and standard deviation for the multivariate normal distribution MU and SD respectively.

MU = sum (mu1,...,mun)

SD = sqrt(transpose(sd)*sigma*sd)

Then calculate the 99th percentile for the multivariate (which is what I really want) using this MU and SD and the normal distribution. Call this 99VaR.

I have seen that one can get the same answer as 99VaR by using:

sqrt(transpose(VaR)*sigma*VaR)

I am just not sure of the maths as to why?

If this works for the multivariate normal - does it work for other multivariate distributions?

Any comments are most welcome