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Re: Determining if samples are normal


From: Mike Miller
Subject: Re: Determining if samples are normal
Date: Tue, 27 Sep 2005 11:35:05 -0500 (CDT)

On Tue, 27 Sep 2005, Paul Koufalas wrote:

Michael Creel wrote:

This is related to the central limit theorem. The average of the sum of n centered random variables, multiplied by the square root of n, converges in distribution to a normal random variable. There are a few technical conditions that need to be satisfied, but they hold for this example. There is no such general result for multiplication of random variables.

Robert and Michael, if I recall correctly, there *is* a general result for multiplication of random variables: convergence in distribution to a uniform random variable.

Bear in mind I'm recalling a whiteboard discussion that happened in about 1995 with a certain Prof Ken Lever, while I was a Masters student, so I could be wrong!!!


Under certain conditions, if we take logs, then we have the sum instead of the product of a collection of random variables. The sum converges by the CLT to normal, so the product must be converging to lognormal, not to uniform:

http://mathworld.wolfram.com/LogNormalDistribution.html

Note the assumption of "a large number of independent, identically- distributed variables." We didn't mention independence and identical distribution before.

This is interesting, but getting far off topic, no?

Mike



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