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Q: Simulating a vector that as known variance matrix ( Answered ,   0 Comments )
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 Subject: Simulating a vector that as known variance matrix Category: Science > Math Asked by: mathdumbie-ga List Price: \$25.00 Posted: 28 Oct 2006 21:13 PDT Expires: 27 Nov 2006 20:13 PST Question ID: 777962
 ```How would you simulate a vector or random variables that has a known mean vector and a known variance-covariance matrix?```
 ```Hi easy way is this: 1) Take n independent normal variables with variance 1 and mean 0 n is dimension of your linear space arrange them inro a vector v 2) make a linerar transformation X.i = L.i/j * v.j 3) L is a matrix which you get by diagonalising your given variance (or rather it's inverse) 4) X.i = X.i + B.i will chage means as needed. re 3) http://ltcconline.net/greenl/courses/203/MatrixOnVectors/diagonalization.htm http://en.wikipedia.org/wiki/Diagonalizable_matrix re 1) http://en.wikipedia.org/wiki/Multivariate_normal_distribution http://www-math.mit.edu/~panchenk/class443/lectures/lecture4.pdf https://netfiles.uiuc.edu/jimarden/www/Classes/STAT571/chapter3.pdf Hope this will work for you Hedgie```
 mathdumbie-ga rated this answer: `Complete and concise answers. Perfect.`