Re: Add Noise

From: Rich Townsend (rhdt_at_barVOIDtol.udel.edu)
Date: 03/18/04 

Date: Thu, 18 Mar 2004 15:50:26 -0500

Richard Maine wrote:
> Rich Townsend <rhdt@barVOIDtol.udel.edu> writes:
>
>
>>Joost VandeVondele wrote:
>>
>>>tholen@antispam.ham wrote in message news:<dJg6c.7907$h85.3597@twister.socal.rr.com>...
>
>
>>>noisy_vector=vector
>>>DO i=1,N
>>>call random_number(noise)
>>>noisy_vector=noisy_vector+(noise -0.5)*scale
>>>ENDDO
>>
>>Still ain't Gaussian...
>
>
> But by the central limit theorem, it approaches Gaussian as N
> approaches infinity (assuming you normalize scale appropriately).

You're right, I don't think I read or understood the code properly. As
you point out, though, there is a gotcha in normalizing scale properly;
if scale is kept independent of N, then the standard deviation of the
resulting Gaussian distribution will grow as SQRT(N).

This is, of course, why a random walk can get a particle from A to B. It
is also why the so-called 'law of averages' -- that a heads is highly
probable after tossing 6 consecutive tails -- is total bunk. And also
why the phenomenon of 'gamblers ruin' will mean that Casinos will always
win (assuming they are richer than the punters), even when the odds are
completely fair.

cheers,

Rich

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