Jerry Avins
Guest
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 Posted:
Mon Jan 03, 2005 11:35 pm Post subject:
Re: PDF of Quantization Error |
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Stan Pawlukiewicz wrote:
| Quote: | Jerry Avins wrote:
Clay S. Turner wrote:
"Country_Chiel" <Chiel@bothy.nichts.co.uk> wrote in message
news:1104565931.539467@ftpsrv1...
If you use the central limit theorem everything is Guassian
eventually!
Actually no.
You can add Cauchy random vars together to your heart's content, and
the answer will always be a Cauchy random varible. This distribution
is also known as a Lorentzian distribution which shows up in cases of
resonance. I.e. the amplitude verses frequency function for a
emission line produced by an atom as an electron moves from a high to
a low energy level.
The shape of the PDF is close enough to Gaussian so the difference falls
within the tolerance we normally allow when matching practice to theory.
Because of that, the exception is easily overlooked. Peruse
http://www.math.hope.edu/~tanis/Phoenix/Cauchy1.html
Jerry
I don't agree Jerry. You have to clip observations to generate
histogram. It really doesn't behave like a Gaussian.
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I didn't say it behaves like Gaussian; very few limited sets of data do.
Since departures from ideal Gaussian are usual for actual observations,
most of us develop a great deal of estimation tolerance for just about
any departures other than pronounced skew or bimodalism. It's not
unusual for Cauchy distributions to fall within that broad tolerance
when looked at casually.
I thought that's what I said. Sorry.
Jerry
--
Engineering is the art of making what you want from things you can get.
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