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Re: Determining if samples are normal


From: Quentin Spencer
Subject: Re: Determining if samples are normal
Date: Mon, 26 Sep 2005 12:42:47 -0500
User-agent: Mozilla Thunderbird 1.0.6-1.1.fc4 (X11/20050720)

Robert A. Macy wrote:

Sorry, to jump in where I have very little knowledge and
understanding, but doesn't the sum preserve the
distribution?  Seems counter intuitive to have the sum
change the distribution if it's identical.  Isn't it
multiply that makes it triangular?

The PDF of a sum of two random variables is the convolution of their respective PDFs. It just happens that the convolution of a gaussian function with a gaussian function is a gaussian function (you could say that it is to convolution what the exponential function is to integration/differentiation), so the sum of two normals is also normal (but with a different variance), but the sum of any two other random variables is definitely not normal.

-Quentin



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