You want to generate an nx1 vector of normal random numbers u ~ N(0,S), where n x n S is the variance-covariance matrix of u. Let A'A = S, then A^-1u ~ N(0,I), where I is the n x n identity matrix. Notice e = A^-1 u ~ N(0,I) is rather easy to generate since each element of e is just iid normal. Just use @rnorm or nrnd to generate the elements of the e. After generating e you can transform e to u by the relationship u = A e. There are many A's that satisfies A'A = S. A popular way to decompose S is using Cholesky decomposition. Here I have an example of how to do this. (If u has non-zero means, you can add each column of u by its mean.)Hi everyone !
Is there some mean to get a random sample from a Normal Bi-variate distribution (known means, std.dev. and rho) ?
Thank you !
Regards
Phil
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'S contain the !n x !n covariance matrix
' u ~N(0,S)
' set parameters
!n = 2 ' number of variables
!t = 100 ' number of random !n-pairs
sym(!n,!n) S
S.fill 1,-.2,3
matrix A = @cholesky(S)
matrix(!n,!t) e
nrnd(e)
matrix u = @transpose(A*e)
' if you need to move u into workfile series you
' can use the command MTOS
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nrnd(e)