Re: Summing Noise Sources


"John Corbett" <corbett@xxxxxxxxxxxx> wrote in message
news:corbett-0410071446140001@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx
In article <ldidnWaSjZ1_iZzanZ2dnUVZ_ualnZ2d@xxxxxxxxxxx>, "Arny Krueger"
<arnyk@xxxxxxxxxx> wrote:

There's a theorum that says that the more uncorrelated noise sources that
you sum up, the more the statistics of the sum approaches gaussian.

That "theorum" is obviously false. Merely being uncorrelated is far too
weak a condition on the quantities being summed to justify what is
claimed. Much stronger conditions (e.g., independent and
identically-distributed random variables with finite variance) are
required for the usual Central Limit Theorem.

I love it. Corbett jumps in with his usual hair-splitting. Example: in
Corbett-land, there's no relationship between being uncorrelated and being
independent.

I seem to recall that 12 independent noise sources with uniform amplitude
distributions sum up to something that is very, very close to being
gaussian.

Wrong.

Now Corbett sees the identical same word he used - independent, and its
still not right! LOL!

For starters, you need the additional assumption that those 12
noise sources have the *same* uniform distribution, otherwise you can get
a sum that is nowhere near gaussian.

More hair-splitting, this time presuming that the 12 noise sources would
logically be chosen with different uniform distributions.

Here's a news flash for you John, people don't often write paragraphs for
PhD theses when they are writing casual Usenet posts.

John, you've got a proven technique for not making mistakes on Usenet, you
don't post enough to be worth talking about.

To be more exact, google searching shows that you've made 76 posts in all
time, with a whopping approximate 50% or 36 related to me.

Did I scare your mother while she was carrying you or what? ;-)

Even with that condition it doesn't work very well.
The distribution of the sum is not very close to a normal (gaussian)
distribution, especially in the tails. Other methods are both faster and
more accurate, and texts that even mention this scheme at all do so only
as an example of a method *not* to use for generating normally-distributed
random quantities.


.

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