On Wed, 06 Sep 2000 11:32:54 -0400, Art Kendall
<[EMAIL PROTECTED]> wrote:
> would someone name some physical or social phenomena where the measurements
> follow a Cauchy distribution?
>
> "Anon." wrote:
>
< snip, re: "not consistent" estimators >
> > How about the universal counterexample, the mean of a Cauchy
> > distribution? It's simple if you present it as the ratio of two
> > standard normal distributions.
> >
> > Bob
- From Philip Bevington's book "Data Reduction...",
(page 49, 1969 edition) concerning the Lorentzian
(Cauchy) distribution, "which occurs quite often
in nuclear physics data reduction."
"It is an appropriate distribution for describing data
corresponding to resonance behavior, such as the
variation with energy of the cross section of a nuclear
reaction or the variation with velocity of absorption
of radiation in the Mossbauer effect."
An example in English: I think this underlies the delicacy needed in
the control of a nuclear power plant (in the most common U.S. design).
Control rods, which consist of neutron-absorbing material, don't have
to move very far in order to make a big difference. You don't get the
usual, added stability of taking averages ('average cross section' for
the capture of a neutron) when you average Cauchy variates. The
distribution has a fat tail. The variance is infinite, and the
standard deviation of the mean remains equal to the standard deviation
of a point. (I hope my description of it has not butchered the
science.)
--
Rich Ulrich, [EMAIL PROTECTED]
http://www.pitt.edu/~wpilib/index.html
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