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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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- Re: Determining if samples are normal, (continued)
- Re: Determining if samples are normal, Robert A. Macy, 2005/09/26
- Re: Determining if samples are normal, Quentin Spencer, 2005/09/26
- Re: Determining if samples are normal, Mike Miller, 2005/09/26
- Re: Determining if samples are normal, Przemek Klosowski, 2005/09/26
- Re: Determining if samples are normal, Robert A. Macy, 2005/09/26
- Re: Determining if samples are normal, Mike Miller, 2005/09/26
- Re: Determining if samples are normal, Raymond E. Rogers, 2005/09/26
- Re: Determining if samples are normal, Mike Miller, 2005/09/27
- Re: Determining if samples are normal, Michael Creel, 2005/09/27
- Re: Determining if samples are normal, Paul Koufalas, 2005/09/27
- Re: Determining if samples are normal,
Mike Miller <=
- Re: Determining if samples are normal, Mike Miller, 2005/09/26
- Message not available
- Re: Determining if samples are normal, Mike Miller, 2005/09/26
Re: Determining if samples are normal, Joe Koski, 2005/09/25
Re: Determining if samples are normal, Paul Kienzle, 2005/09/26