In article <[EMAIL PROTECTED]>,
Radford Neal <[EMAIL PROTECTED]> wrote:
>In article <[EMAIL PROTECTED]>,
>Eric Bohlman <[EMAIL PROTECTED]> wrote:
.......................
>>What would be good
>>similar examples for distributions that are symmetric but not normal (for
>>students who aren't yet sophisticated enough for the Cauchy distribution to
>>be a good example)?
Why are they not sophisticated enough for the Cauchy distribution?
It is the distribution of the tangent of a random angle, or if
one wants to add a location parameter, the place where the ray
from a lighthouse hits a straight shore.
>This is difficult, since there's usually no reason for a real
>distribution to by symmetric. Perhaps errors in measurement of
>longitude?
It was assumed, and as we now know mistakenly, that errors
of measurement were symmetric. Massive amounts of linear
and non-linear least squares was used in the 19th century
on astronomy and geodesy. One of the proofs of normality
by Gauss assumed that errors of astronomical observation,
and Gauss considered himself to be primarily an astronomer,
were spherically symmetric and independent.
>----------------------------------------------------------------------------
>Radford M. Neal [EMAIL PROTECTED]
>Dept. of Statistics and Dept. of Computer Science [EMAIL PROTECTED]
>University of Toronto http://www.cs.utoronto.ca/~radford
>----------------------------------------------------------------------------
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
[EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558
.
.
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