[PD] Box Muller Gaussian noise

[Charles Henry]

On Sun, Mar 16, 2008 at 2:49 PM, Charles Henry <czhenry at gmail.com> wrote:
> our cdf (cumulative dist function)
> G(Z)=P( Z<r^2 )= integral ( r^2 = 0 to Z, 1/sigma^2 * e^-(r^2/sigma^2) d(r^2)
>
> G(Z)=1 - e^-(Z/sigma^2)


> Take U1=Z on [0,1] , take U2 on [0,1]

Actually, it makes more sense for U1 to be distributed on [0, 1)
Because we need to take Z to be a finite number, the range of G(Z) is [0,1)
Then, the fine details start to make a litte more sense.

> Notice, the sigma comes out in front, and the variable (1-U1)  is
> distributed uniformly on [0,1] also.  Hence, it can be simplified to
> another uniform variable U3, or whatever.

Actually, this would say, (1-U1) is uniformly distributed on (0,1]
which is more consistent with what we want, since we take the ln of
this number.

Chuck