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How to generate Random Vectors given Covariance Matrix?

Started by Yanjun Yan March 30, 2003
Hi, All:

Do you know how should I generate the Random Vectors given the Covariance
Matrix?

Or in general, how should I realize the correlation between Random variables?

eg:
X=[x1,x2]
Covariance Matrix is[1,0.5;0.5,1]

I want to generate 1000 samples of X, what should I do?

Thanks a LOT!

Kitty




Hi,
There is a procedure, where you do cholesky
decomposition of the required covariance matrix and
multiply the generated random numbers with a
triangular matrix obtained from cholesky
decomposition.
If you need only for two variables, this should reduce
to a simple formula.

You can get more info in a statistics book or random
process book.

Navan --- Yanjun Yan <> wrote:
> Hi, All:
>
> Do you know how should I generate the Random Vectors
> given the Covariance
> Matrix?
>
> Or in general, how should I realize the correlation
> between Random variables?
>
> eg:
> X=[x1,x2]
> Covariance Matrix is[1,0.5;0.5,1]
>
> I want to generate 1000 samples of X, what should I
> do?
>
> Thanks a LOT!
>
> Kitty
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