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From: "John D'Errico" <woodchips@rochester.rr.com>
Newsgroups: comp.soft-sys.matlab
Subject: Re: Limiting case of an exponential distribution
Date: Sat, 10 Jan 2009 15:43:02 +0000 (UTC)
Organization: John D'Errico (1-3LEW5R)
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ImageAnalyst <imageanalyst@mailinator.com> wrote in message <d2fc0576-1aec-418f-9cdd-154728bf35e2@s9g2000prm.googlegroups.com>...
> Limiting how?  Which coefficient are you going to send to the limit of
> 0 or infinity, and then once you do that you'll observe a Gaussian?
> Mathematically I just don't see it.

As the shape parameter of the gamma (k - 1 = 9, from
the exponent of t) goes to infinity, the gamma can be
said to approach a normal distribution. See that the
skewness is 2/sqrt(k), and the excess kurtotis is 6/k. As
these two moments go to zero, the distribution starts to
look more and more normal.

But here that parameter is fixed. It is not allowed to
approach +inf. So it makes no sense to talk about the
limiting behavior. As I suggested, you can make the
simple approximation of using a normal with the
indicated mean and variance, but it will not be a
terribly good approximation. It will also yield a
significant probability that such a normal deviate
will be less than zero.

John