How to draw bivariate random vector (v,u) which is bivariate normal, but with a correlation which depends on a third variable x?

Dear all,

I would like to simulate some data: a bivariate random vector (v,u) which is bivariate normal, but with a correlation which depends on a third variable x.

Suppose I have 10 x 1 vector of x_is. I can define the correlation as

p(x_i)=[exp(x_i)-1]/[exp(x_i)+1]

such that it each p(x_i) with the interval [-1,1].

Then I would like to draw a bivariate random vector of size 10 (v,u) with correlation matrix (1 , p(x_i) \ p(x_i) , 1). Essentially I would like to have a distinct Corr(v_i,u_i)=p(x_i).

Anyone has any ideas?

Thank you!

Riju

Share on FacebookPlus on Google+