Re: radial gaussian distribution

[Mike Miller]

On Tue, 20 Sep 2005 address@hidden wrote:

> Be careful, Roberto! The "solution"
>
>  r = R*randn(N,1);
>
> (followed by "x = r.*sin(phi); y = r.*cos(phi);" to generate 
> corresponding x and y coordinates) posted by Shai Ayal is in fact not 
> correct for what you want!

I think it was correct.  The Euclidian distance of (x,y) to (0,0) is r, as 
Roberto requested.

I think the disagreement here is because of one 'n' above.  This would not 
work...

r = R*rand(N,1);

...and if used like this,

phi=rand(N,1)*2*pi;
x = sqrt(-2*log(r)).*sin(phi);
y = sqrt(-2*log(r)).*cos(phi);

it would produce bivariate normal (x,y):

http://mathworld.wolfram.com/Box-MullerTransformation.html

but this...

r = R*randn(N,1);
phi=rand(N,1)*2*pi;
x = r.*sin(phi);
y = r.*cos(phi);

Seems to do what was requested because 'r' is the distance from (x,y) to 
(0,0) and it has a normal distribution.

Mike



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