Path: news.mathworks.com!not-for-mail 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) Lines: 22 Message-ID: <gkafm6$9mt$1@fred.mathworks.com> References: <5e3bfffd-9cf6-417e-8c92-fe40feedcd71@o40g2000prn.googlegroups.com> <d2fc0576-1aec-418f-9cdd-154728bf35e2@s9g2000prm.googlegroups.com> Reply-To: "John D'Errico" <woodchips@rochester.rr.com> NNTP-Posting-Host: webapp-05-blr.mathworks.com Content-Type: text/plain; charset="ISO-8859-1" Content-Transfer-Encoding: 8bit X-Trace: fred.mathworks.com 1231602182 9949 172.30.248.35 (10 Jan 2009 15:43:02 GMT) X-Complaints-To: news@mathworks.com NNTP-Posting-Date: Sat, 10 Jan 2009 15:43:02 +0000 (UTC) X-Newsreader: MATLAB Central Newsreader 869215 Xref: news.mathworks.com comp.soft-sys.matlab:510769 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