Generate Elliptical Distribution from Box-Muller Transform

[ireland01]

Can i use box muller transform to generate a distribution with two different sigma (i.e. sigma_x and sigma_y)?

I want to generate a random gaussian angle (C) relative to z axis on circle plane, then set the angle relative to the x, A and y axis, B, wrt to the original angle.
However, I want the output to be elliptical on x/y plane...

Some pseudo code would help.

 

[Lord Crc]

If X is normal with zero mean and std dev = 1, then you can transform it into a random variable Z with mean u and std dev sigma as follows:

Z = sigma*X + u

The Box-Muller transform gives you two random variables which are standard normally distributed iirc, so just apply the above transformation to each.