Stan Pawlukiewicz wrote:> 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.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. �����������������������������������������������������������������������