Re: multivariate gaussian distribution (Code)

[Przemyslaw Sliwa <sliwa@euv-frankfurt-o.de>]

Dear All,

There are several thing I cannot understand in the code. I suppose it has
been designed to handle real random vectors for multivariate normal
distribution. Therefore at least two points:

1. Why did you (Emmanuel) use the Eigenvalue decomposition of the
covariance matrix. This method is extremely inefficient with the gsl
eigenvalues code. One shall (I do) use the Cholesky decomposition of the
covariance matrix in order to compute the lower triangular matrix L of the
form Cov = LL' This procedure is described in several books e.g.
Harville's "Matrix Algebra from a Statistician's perspective".

2. Why do you use this Box Mueller Algorithm? My point is: if you have a
vector X of independent, normally distributed variables (Covariance matrix
equals identity matrix) the product P = LX is always normally distributed
with covariance matrix Cov, since (assuming E(X) = 0) E(PP') = E(LX(LX)')
= E(LXX'L) = LIL' = Cov. Similar to this method one can simulate the whole
family of elliptically countered distributions (like Bessel, generalized
Lapalce, t-distributions).

Did I miss something?

Thanks for explanations,

Kind regards,

Przem