Re: convolving noise with noise will get Gaussian? what does that imply?

From: Herman Rubin (hrubin_at_odds.stat.purdue.edu)
Date: 11/03/04 

Date: 3 Nov 2004 14:55:25 -0500

In article <f56893ae.0411030026.1385213f@posting.google.com>,
Rune Allnor <allnor@tele.ntnu.no> wrote:
>"kiki" <lunaliu3@yahoo.com> wrote in message news:<cm8mci$sjo$1@news.Stanford.EDU>...
>> Suppose I have a segment of data, which is basically random numbers between
>> 0 and 1. I call it "f".

>> Doing "f" -- the noise -- self convolution several times, the resultant
>> data, if plotted, is of Gaussian shape.

The convolution of identical distributions with second
moments is APPROXIMATELY normal, the approximation becoming
better with the number convolved.

The convolution of two distributions is never normal
unless both are normal.

These two theorems may seem paradoxical, but they are
both true. 

-- 
This address is for information only.  I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@stat.purdue.edu         Phone: (765)494-6054   FAX: (765)494-0558
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